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related_results_labels_thumbs({"version":"1.0","encoding":"UTF-8","feed":{"xmlns":"http://www.w3.org/2005/Atom","xmlns$openSearch":"http://a9.com/-/spec/opensearchrss/1.0/","xmlns$blogger":"http://schemas.google.com/blogger/2008","xmlns$georss":"http://www.georss.org/georss","xmlns$gd":"http://schemas.google.com/g/2005","xmlns$thr":"http://purl.org/syndication/thread/1.0","id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721"},"updated":{"$t":"2017-01-23T10:01:30.102-08:00"},"category":[{"term":"Fluid Mechanics"},{"term":"Machine Design"},{"term":"Mechanics"},{"term":"Electrical Machines"},{"term":"Hydraulic Machines"},{"term":"Structural"},{"term":"Thermal Engineering"},{"term":"Automobile"},{"term":"Manufacturing"},{"term":"Aerospace"},{"term":"Power Plant"},{"term":"Thermodynamics"},{"term":"Wind Power"},{"term":"Mechanical"}],"title":{"type":"text","$t":"Learn Engineering"},"subtitle":{"type":"html","$t":"An educational venture to make fundamentals of engineering strong"},"link":[{"rel":"http://schemas.google.com/g/2005#feed","type":"application/atom+xml","href":"http:\/\/www.learnengineering.org\/feeds\/posts\/default"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/-\/Machine+Design?alt=json-in-script\u0026max-results=10"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/search\/label\/Machine%20Design"},{"rel":"hub","href":"http://pubsubhubbub.appspot.com/"},{"rel":"next","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/-\/Machine+Design\/-\/Machine+Design?alt=json-in-script\u0026start-index=11\u0026max-results=10"}],"author":[{"name":{"$t":"sabinm"},"uri":{"$t":"http:\/\/www.blogger.com\/profile\/04997465892285104768"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"16","height":"16","src":"http:\/\/img1.blogblog.com\/img\/b16-rounded.gif"}}],"generator":{"version":"7.00","uri":"http://www.blogger.com","$t":"Blogger"},"openSearch$totalResults":{"$t":"12"},"openSearch$startIndex":{"$t":"1"},"openSearch$itemsPerPage":{"$t":"10"},"entry":[{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-7104603657198055370"},"published":{"$t":"2015-08-24T22:45:00.000-07:00"},"updated":{"$t":"2016-04-28T01:18:27.266-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Automobile"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Mechanics"}],"title":{"type":"text","$t":"Manual Transmission, How it works ?"},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cp\u003EManual transmission, or simply a gearbox, has been serving automobiles well for many decades. Even today it’s the most popular form of transmission. Globally manual transmission accounts for 52% of market share as per 2013 data. In this video, we’ll give a conceptual introduction on the workings of an actual manual transmission with a reverse gear.  \u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/wCu9W9xNwtI\" frameborder=\"0\" allowfullscreen\u003E\u003C\/iframe\u003E\u003C\/div\u003EA detailed webpage version of the video is given below.\u003C\/p\u003E\u003Chr\u003E\u003Cbr\u003E   \u003Ch2\u003EWhy the Transmission is Required?\u003C\/h2\u003E\u003Cp\u003EThe basic question, is why transmission is required in an automobile?  The power generated by the engine flows through the transmission before it reaches the drive wheels.The basic function of the transmission is to control the speed and torque available to the drive wheels for different driving conditions.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/1.bp.blogspot.com\/-cWVnefU6xVc\/Vdwwze3VBPI\/AAAAAAAADl4\/7GiQwLtraI8\/s1600\/drive_train_automobile.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.1 Power flow in an automobile; the power from engine to drive wheels is transferred through a drive train \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E   For example, if you want to climb a hill, you need more torque. By reducing the speed at the transmission, we will be able to achieve higher torque for the same power input. This is simply conservation of energy. Power transmission through a shaft is torque times angular velocity of the shaft. When you reduce the speed of the shaft, it will automatically result in increase in the torque transmission. Conversely, if the torque demand is low , we can increase the transmission speed. These 2 cases are depicted in Fig.2. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-lok3KAwSRos\/VdAaRzzXwfI\/AAAAAAAADi0\/jav35buRkc0\/s1600\/transmission_use.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.2 During a climb the wheels need more torque; during descent the reverse is the case\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E\u003Ch2\u003EThe Basic Working Principle \u003C\/h2\u003E\u003Cp\u003ENow let’s look at its inner workings. Manual transmissions work on the simple principle of gear ratio. As shown in Fig.3 a different output speed can be achieved by meshing gears of different size. The speed ratio is given by the simple equation shown in the figure (N represents speed, T represents number of teeth). \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-RLhrqywZaRI\/VdppLlFYZiI\/AAAAAAAADlo\/eDmDgmWxyyg\/s1600\/Basic_Principle_Gear_ratio.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.3 The basic principle of a gear pair \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E  \u003Ch2\u003ESliding Mesh Transmission\u003C\/h2\u003E\u003Cp\u003ESliding mesh is the one of the earlier type of manual transmission technology, and the one which is easiest to understand. The most basic slidngmesh transmission mechanism is shown in the Fig.4. Here the input and output shafts are connected through a counter shaft. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-NHpPSSxIaJc\/VdAaRUjONUI\/AAAAAAAADik\/IqUWi3Je_YI\/s1600\/sliding_mesh_transmission_operation.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.4 First and second gear in a sliding mesh transmission; the red line represents the power flow  \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003EThis mechanism can operate under 2 different configurations. In the firs configuration, the output shaft will turn at a slower speed than the input. Just by sliding output gear and connecting the output shaft with the input will result in the second configuration. It is clear that, here the input and out will turn at the same speed. Direction of the power flow is represented as red dotted lines in the Fig.4.   \u003Cp\u003E A 3-speed mechanism will look as shown in the Fig.5. For the gear meshing shown in the figure, the output shaft will rotate at its slowest speed (1\u003Csup\u003Est\u003C\/sup\u003E Gear).It is clear that just by sliding the gears we can achieve different transmission ratios, such as 2\u003Csup\u003End\u003C\/sup\u003E and 3\u003Csup\u003Erd\u003C\/sup\u003E gears.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-8rfOXRwAt4c\/VdA2zMfDFZI\/AAAAAAAADjg\/rv1rrqu3bfc\/s1600\/Three_Speed_Sliding_Mesh.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.5 Three speed sliding mesh transmission: first gear is shown in the figure \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E   \u003Cp\u003EThe sliding mesh transmission is good for controlling the speed, but they have an inherent disadvantage.  It’s quite tricky to slide from one gear and engage with another gear. A technology known as double clutching should be used for achieving a smooth slide of gears. The driver should possess a good skill to do an effective double clutching. Maintenance associated with the double clutch transmissions are quite frequent too.\u003C\/p\u003E\u003C\/p\u003E   \u003Ch2\u003ESolving the Sliding Problem – Synchromesh Transmission\u003C\/h2\u003E\u003Cp\u003E\u003Cp\u003EThe synchro mesh transmission permanently solves this problem. Here the gears are always in mesh, but with a major difference. Here the output gears are loosely connected to the shaft. You can see from Fig.6 that there is a small clearance between the output gears and shaft. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/2.bp.blogspot.com\/-6zmAxnjX_mY\/VdAxIGzVYTI\/AAAAAAAADjI\/XIlbADqlUTY\/s1600\/synchromesh.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.6 Synchromesh transmission: Here the gear pairs are always in mesh \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E If we connect only one gear to the shaft at a time, the shaft will have the speed of the connected gear.\u003C\/p\u003E\u003Ch3\u003EUnderstanding the basis using a Hypothetical connector\u003C\/h3\u003E\u003Cp\u003EWe will first use a hypothetical connector to illustrate how different gear ratios work in the sycnhromesh transmission. Later on we will move to the actual technology. With the help of the hypothetical connector, different gear ratios are illustrated in Fig.5. It is interesting to note that in 4th gear the input and output shafts are directly connected. This means the output and input shaft will have the same speed in 4th gear. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/2.bp.blogspot.com\/-tmRDh4SUpm0\/VdnA0B50ZcI\/AAAAAAAADj4\/a5o_bZjO4CM\/s1600\/Hypothetical_Connector.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.7 First and Fourth gear are illustrated in this figure with help of a hypothetical connector \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003EThe art of locking a loosely held gear to the shaft effectively and smoothly lies at the heart of the manual transmission. Let’s see how this is done in actual practice.\u003C\/p\u003E  \u003Ch3\u003ESynchronizer Cone-Teeth Arrangement\u003C\/h3\u003E\u003Cp\u003EFirst of all, the main shaft gears have a synchronizer cone-teeth arrangement as illustrated in Fig.8.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-5swUB5IMv9U\/VdnA0McmC9I\/AAAAAAAADj8\/OT2nilQ1Sv4\/s1600\/Synchronizer_cone_teeth.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.8 Synchronizer cone teeth arrangement of synchromesh transmisson \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E A hub is fixed to the shaft. A sleeve that is free to slide over the hub is also used in this system. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/4.bp.blogspot.com\/-UnIAp-090X4\/VdnD51rZXjI\/AAAAAAAADkM\/rfsXKixaAMw\/s1600\/Sleeve_Hub.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.9 When the sleeve and synchronizer teeth are engaged the locking action can be achieved \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003EIt is clear that, if the sleeve gets connected with the teeth of the synchronizer cone, the gear and shaft will turn together, or the desired locking action will be achieved. But during the gearbox operation, the shaft and gear will be rotating at different speeds. So such a locking action is not an easy task.\u003C\/p\u003E  \u003Ch3\u003EUse of Synchronizer ring\u003C\/h3\u003E\u003Cp\u003EA synchronizer ring helps to match the speed of the gear with that of the shaft. The synchronizer ring is capable of rotating along with the hub, but is free to slide axially. Before moving the sleeve, the clutch pedal is pressed. This way power flow to the gear is discontinued.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/2.bp.blogspot.com\/-wS0Wc9_Mygs\/VdnFe49XtyI\/AAAAAAAADkY\/95Cvg47zY5g\/s1600\/Synchronizer_Ring.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.10 A synchronizer cone is placed between a hub and synchronzier cone \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003EWhen we move the sleeve, the sleeve will press the synchronizer ring against the cone. Due to the high frictional force between the synchronizer ring and cone, the speed of the gear will become the same as the shaft. At this time, the sleeve can be slid in further, and it will get locked with the gear. Thus, the gear gets locked with the shaft in an efficient and smooth way. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/4.bp.blogspot.com\/-CahbbUu1xQI\/VdnIxmlAWYI\/AAAAAAAADk0\/iLGkgx_vqaA\/s1600\/synchromesh_operation.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.11 Movement of sleeve brings the synchronizer teeth and sleeve to the speed, after that the locking is achieved \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E   \u003Ch2\u003EDifferent Gear Ratios \u003C\/h2\u003E\u003Cp\u003EWhat we have seen in last section was  the technology behind the 2\u003Csup\u003End\u003C\/sup\u003E  gear. In the same way the other gear ratios are also achieved. The details are described in this session.    \u003Ch3\u003EUnder Drive – 1\u003Csup\u003Est\u003C\/sup\u003E, 2\u003Csup\u003End\u003C\/sup\u003E and 3\u003Csup\u003Erd\u003C\/sup\u003E\u003C\/h3\u003E\u003Cp\u003EIn under drive the output shaft turns at a lower speed than the input.  For the manual transmission technology we are explaining 1\u003Csup\u003Est\u003C\/sup\u003E , 2\u003Csup\u003End\u003C\/sup\u003E and 3\u003Csup\u003Erd\u003C\/sup\u003E gear ratios fall under the under drive category. The following figure depicts the sleeve motion required for 1st and 3rd gear. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-SEqzty0X9tc\/VdnHQgmUUrI\/AAAAAAAADkk\/EE4x0G2FoaU\/s1600\/1st_3rd_Gear.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.12 The first and third gear of a manual transmission \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E \u003C\/p\u003E\u003Ch3\u003EDirect Drive\u003C\/h3\u003E\u003Cp\u003EAs the name suggests in direct drive, the output and input shafts turn at the speed. For this purpose the output and input shafts are directly coupled using the synchronizer cone-sleeve mechanism. The hub is fixed to the output shaft, when the sleeve gets connected with the synchronizer teeth of the input shaft, they get coupled together. During the direct drive, the sleeve at the third gear position (2nd part Fig.12) should move to left side.\u003C\/p\u003E\u003Ch3\u003EOver Drive\u003C\/h3\u003E\u003Cp\u003EA 5th gear is used to turn the output shaft at a higher speed than the input shaft. You can note here that unlike the other gear pairs, in 5th gear the output shaft gear is smaller than the counter shaft gear. This generates the overdrive scenario. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-LLUDQzO9YpU\/VdnKkSCg32I\/AAAAAAAADlA\/QtaSHeNSrp0\/s1600\/Over_drive.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.13 The arrangement of 5th gear \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E You can note more difference in the 5th drive configuration, the output gear is fixed to the shaft and the counter shaft gear is loosely connected. As a result synchroizer ring – sleeve mechanism is arranged on the counter shaft. The sole purpose of such an arrangement is to accommodate the reverse gear mechanism. We will see that in next session. \u003C\/p\u003E\u003Cp\u003EThe sleeve motion is controlled by a shift stick . You can also  see the mechanism used for controlling the sleeve with the shift stick. You can note that using this mechanism, not more than one sleeve will be engaged with the output gears. That is important, since engaging 2 sleeves at a time will lead to an impossible turning condition. \u003C\/p\u003E\u003Ch3\u003EThe Reverse Gear\u003C\/h3\u003E\u003Cp\u003ENow let’s see how the reverse gear works? The reverse gear uses a 3-gear arrangement, as shown. Out of those, one is the idle gear. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/4.bp.blogspot.com\/-lozFxoQJ4mc\/VdnZD6KAZeI\/AAAAAAAADlU\/17PeizlLiWY\/s1600\/Reverse_Gear.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.14 The three gear arrangement of a reverse gear \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E It is clear that addition of one more gear will turn the output shaft gear in the reverse direction. For engaging the reverse gear the idle gear is pushed and connected to the other 2 gears. Thus  the required output shaft rotation in the reverse direction can be achieved. Please note here that the reverse gear does not have a synchronizer ring mechanism. This means that, the gearbox rotation has to stop completely before applying the reverse gear. \u003C\/p\u003E\u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/1.bp.blogspot.com\/-mgGikPzE4es\/VdnZDoSLKfI\/AAAAAAAADlQ\/R5xcplEEzJw\/s1600\/Reverse_Working.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.15 The idle gear is pushed and connected with the other 2 gears to achieve the reverse operation \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003Cp\u003EYou might have noticed that in reverse gear, your vehicle moves in a very low speed. As you can see from the figure the three gear arrangement gives speed reduction in 2 stages. This results in very low output speed (high torque). Generally the reverse has a gear ratio of 4:1 (input speed : output speed). \u003C\/p\u003E   \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/7104603657198055370"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/7104603657198055370"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2015\/08\/Manual-Transmission-Working.html","title":"Manual Transmission, How it works ?"}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"https:\/\/img.youtube.com\/vi\/wCu9W9xNwtI\/default.jpg","height":"72","width":"72"}},{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-7188373855658821700"},"published":{"$t":"2014-11-19T03:33:00.000-08:00"},"updated":{"$t":"2016-04-28T01:19:35.261-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Automobile"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Mechanics"}],"title":{"type":"text","$t":"Torsen Differential, How it works ?"},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cp\u003ETorsen is a trade mark of the JTEKT Corporation.  The Torsen differential has many patented components and,  is the most unique and ingenious method of providing differential action while overcoming the traction difference problem. This article gives a logical introduction to the working of Torsen differential.\u003C\/p\u003E  \u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe width=\"720\" height=\"405\" src=\"\/\/www.youtube.com\/embed\/JEiSTzK-A2A\" frameborder=\"0\" allowfullscreen\u003E\u003C\/iframe\u003E\u003C\/div\u003E\u003Cp\u003EA detailed webpage version of the video is given below.\u003C\/p\u003E\u003Chr\u003E\u003Cbr\u003E\u003Ch2\u003EThe internal components\u003C\/h2\u003E\u003Cp\u003EThe internal components of a Torsen are quite different from that of a conventional differential. An exploded view of the Torsen is given in Fig.1.   \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"http:\/\/3.bp.blogspot.com\/-Xx4eHtrjh9A\/VJfybu2On3I\/AAAAAAAADV4\/iRkdhsDuG7I\/s1600\/Torsen_componets.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.1 An exploded view of Torsen differential \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E  At the heart of the system lies a specially shaped gear pair assembly. Let’s see the cross sectional shape of these gears at the mating point. As can be seen, one gear is a spur gear, and the other one is a worm gear.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-UPbUXETyMnw\/VJk3DZLU8TI\/AAAAAAAADWI\/CG_ygbOzhbc\/s1600\/Worm_gear_Worm_wheel.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.2 A worm gear-worm wheel mesh lies at the heart of the Toresn; Cross sectional shape of the figure is shown in the second part  \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E  A Torsen works on the simple principle of worm gear- worm wheel; that is a spinning worm gear can rotate the wheel, but the rotating wheel cannot spin the worm gear.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-yLoMYbRSHJY\/VJlAgSxg_AI\/AAAAAAAADWY\/ETau-jdt5wY\/s1600\/Principle_Torsen.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.3 The worm gear- worm wheel principle lies at the heart of the Torsen operation \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E Throughout this discussion, just keep this principle in mind.  A pair of such worm wheels are fitted with the case, so the engine power received by the case is transferred to the worm wheels.  Each end of the wheels is fitted with a spur gear. As a result, a simplified Torsen differential will look as shown in the Fig.4.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"http:\/\/3.bp.blogspot.com\/-a1TFyHpiWXk\/VJlDYJe2vFI\/AAAAAAAADWs\/o40w1cJ3yK8\/s1600\/Basic%2BComponents.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.4 The complete Torsen differential\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003ENow we will go through different driving scenarios and understand how the Torsen manages to operate the vehicle well.\u003C\/p\u003E\u003Ch2\u003EThe Vehicle Moves Straight\u003C\/h2\u003E  \u003Cp\u003EWhen the vehicle moves straight, the worm wheels will push and turn the worm gears. So both the drive wheels will rotate at the same speed.  Please note here that, in this condition the worm wheels do not spin on its own axis.  In this condition, the whole mechanism moves as a single solid unit.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"http:\/\/1.bp.blogspot.com\/-GNsvkKPKlKU\/VJlXKjxHiwI\/AAAAAAAADW8\/DAfUJEZRtO0\/s1600\/Vehicle_moves_straight.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.5 When the vehicle moves straight, worm wheels just push and turn the worm gears at the same speeds. \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E\u003Ch2\u003EThe vehicle takes a right turn\u003C\/h2\u003E\u003Cp\u003EWhen the vehicle is negotiating a right turn, the left wheel needs to rotate at a higher speed than the right wheel. This fact is clear from the Fig.6. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"http:\/\/3.bp.blogspot.com\/-P6vRUp4Snms\/VK-xSBJdauI\/AAAAAAAADXs\/TaSeFEKJavA\/s1600\/Right_Turn.png\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.6 During a right turn the left wheel has to travel more distance \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E  This speed differential is perfectly supported in a Torsen. Please note that the worm wheel is subjected to relative motion not the absolute motion. The worm wheel is fitted between the case and worm gear, so the relative motion between the case and worm gear is what makes the worm gear turn.\u003C\/p\u003E \u003Cp\u003EThe worm gear of the faster left axle will make the corresponding worm wheel spin on its own axis. On the other side, relative to the case the slow right axle is turning in the opposite direction; thus the right worm wheel will spin in the opposite direction. The meshing spur gears at the ends of worm wheel will make sure that, the worm wheels are spinning at the same speed. Thus it guarantees a perfect differential action. Perfect differential action implies equal amount of speed loss and speed gain to the right and left wheels. With the perfect differential the vehiclce will be able to negotiate a smooth turn.   \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"http:\/\/3.bp.blogspot.com\/-TI3DAajiUWQ\/VK-wbYZqCzI\/AAAAAAAADXg\/txJoaW8-vUk\/s1600\/right-turn-Torsen.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.7 The right worm wheel will spin opposite to the right worm wheel; this is due to the opposite relative motion left worm wheel is experiencing  \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003EWhile taking a left turn the worm wheels will spin in an exact opposite way to that shown in Fig.7.\u003C\/p\u003E\u003Ch2\u003EOvercoming the Traction difference problem\u003C\/h2\u003E  \u003Cp\u003ENow let’s try to understand how the Torsen overcomes the drive wheel traction difference problem.  As you might be aware, when your vehicle encounters a situation as shown, the slippery wheel starts to spin very rapidly and will draw the majority of the engine’s power.  As a result, the vehicle will get stuck. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"http:\/\/3.bp.blogspot.com\/-e-GyAKG2SIc\/VK-x7WmmN7I\/AAAAAAAADX0\/3grwVfkt0wM\/s1600\/traction_difference_problem.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.8 A typical traction difference problem a vehicle is experiencing \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E  But, if a Torsen differential is used in this case, as soon as the slippery wheel starts to spin excessively, the speed change will be transferred to the corresponding worm wheel.  The right worm wheel transfers the speed change to the left worm wheel, since they are connected through spur gears.  Here comes the tricky part! The left side worm wheel will not be able to turn the corresponding worm gear, because, as we said, a worm wheel cannot drive a worm gear!  As a result, the whole mechanism gets locked, and the left and right wheels turn together.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"http:\/\/1.bp.blogspot.com\/-ppcL2vQ4SUc\/VK-yJ9eCEBI\/AAAAAAAADX8\/YJ_K2WTYtsQ\/s1600\/Torsen_Locking_action.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.9 The excessive speed of slipping wheel make the system locked due to the 'basic principle of worm gear-worm wheel' \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E This allows a large amount of power to be transferred to the high-traction wheel, and the vehicle can thereby overcome the traction difference problem. To carry the load 2 more worm wheel pairs are added.\u003C\/p\u003E  \u003Ch2\u003EPros and Cons of Torsen\u003C\/h2\u003E\u003Cp\u003EIf you are familiar with the other common technologies used to overcome the traction difference problem, you might have noticed a great advantage of the Torsen.  While the other technologies allow the drive wheel to slip for a limited amount of time before it gets locked, in Torsen the locking action is instantaneous. That means as soon as the vehicle encounters a traction difference track the wheels will get locked. They are also compact compared to their counter parts.\u003C\/p\u003E\u003Cp\u003EFollowing are the some disadvantages of the Toresn type (T1) explained here. \u003Cul\u003E\u003Cli\u003ENoisy\u003C\/li\u003E\u003Cli\u003ECostly\u003C\/li\u003E\u003Cli\u003EMore difficult to assemble\u003C\/li\u003E\u003C\/ul\u003E \u003C\/p\u003E \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/7188373855658821700"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/7188373855658821700"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2014\/11\/Torsen-Differential.html","title":"Torsen Differential, How it works ?"}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"http:\/\/3.bp.blogspot.com\/-Xx4eHtrjh9A\/VJfybu2On3I\/AAAAAAAADV4\/iRkdhsDuG7I\/s72-c\/Torsen_componets.jpg","height":"72","width":"72"}},{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-8219067920659538249"},"published":{"$t":"2014-05-21T19:29:00.001-07:00"},"updated":{"$t":"2016-04-28T01:22:36.998-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Automobile"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Mechanics"}],"title":{"type":"text","$t":"Working of a Limited Slip Differential "},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cp\u003ELimited slip differentials \u003Ci\u003E(LSD)\u003C\/i\u003E are used in automobile to overcome the traction difference problem of drive wheels. In this article working of \u003Ci\u003ELSD\u003C\/i\u003E is explained in a logical manner.\u003C\/p\u003E\u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe width=\"640\" height=\"360\" src=\"\/\/www.youtube.com\/embed\/WeLm7wHvdxQ\" frameborder=\"0\" allowfullscreen\u003E\u003C\/iframe\u003E\u003E\u003C\/div\u003EDetailed webpage version of the video is given below. \u003Chr\u003E\u003Cbr\u003E \u003Ch2\u003EProblem with the Standard Differential\u003C\/h2\u003E\u003Cp\u003EConsider a situation where a vehicle fitted with a standard differential moves straight, and one drive wheel is on a surface with good traction and the other wheel is on a slippery track. In a standard differential the left and right axle rotations are completely independent.  Since one wheel is on a slippery track, the standard differential will make that wheel spin in excessive speed, while the good traction wheel will remain almost dead. This means high power supply to the slippery wheel and low power flow to the good traction wheel. So the vehicle won’t be able to move. \u003C\/p\u003E \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/1.bp.blogspot.com\/-CIho-qj6660\/U3yKuMvd6rI\/AAAAAAAADEo\/FJSlPwuRzR4\/s1600\/traction+difference+problem.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.1 In a standard differential power from the engine is transferred to the wheel with low traction\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E   \u003Cp\u003EOne way to overcome this problem is to limit the independency or relative motion between the left and right axles. \u003Ci\u003ELimited slip differentials\u003C\/i\u003E are introduced for this purpose.  One of the most commonly used LSD technology is \u003Ci\u003Eclutch-pack based\u003C\/i\u003E.\u003C\/p\u003E\u003Ch2\u003EConstructional Features of LSD\u003C\/h2\u003E\u003Cp\u003EFirst we will go through constructional features of LSD.\u003C\/p\u003E   \u003Cp\u003EThe basic components of a standard differential are shown below. It has got pinion gear, ring gear, case, spider gears and side gears.   \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/4.bp.blogspot.com\/-hXj9lVxYwew\/U3yKnc25ZYI\/AAAAAAAADD0\/BKeLzDDYwH0\/s1600\/differential+components.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.2 The basic components of a standard differential\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E To understand working of a standard differential please check \u003Ca href=\"http:\/\/www.learnengineering.org\/2014\/05\/working-of-differential.html\" target=\"_blank\"\u003E\u003Cfont color=\"blue\"\u003Ethis link\u003C\/font\u003E\u003C\/a\u003E . Apart from its basic components a Limited slip differential has got a series of friction and steel plates packed between the side gear and the casing. Friction discs are having internal teeth and they are locked with the splines of the side gear. So the friction discs and the side gear will always move together.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/2.bp.blogspot.com\/-LBJqwJXcfTA\/U3yKnQlQV7I\/AAAAAAAADD8\/sqRZE207ke4\/s1600\/LSD_friction_steel+plates.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.3 It is clear from the figure that steel plates are locked with the case and friction disc with the side gear\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E \u003Cp\u003E Steels plates are having external tabs and are made to fit in the case groove. So they can rotate with the case. \u003C\/p\u003E\u003Cp\u003E If any of the clutch pack assembly is well pressed, the frictional force within them will make it move as a single solid unit. Since steel plates are locked with the case and friction discs with the side gear, in a well pressed clutch pack casing and the clutch pack will move together. Or motion from the casing is directly passed to the corresponding axle.\u003C\/p\u003E    \u003Cp\u003E Space between the side gears is fitted with a pre-load spring. Pre load spring will always give a thrust force and will press clutch pack together. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-3HXZfVOYbz8\/U3yKqzNYYyI\/AAAAAAAADEQ\/YxGwrBYFd70\/s1600\/pre-load+spring+LSD.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.4 Pre-load spring in an LSD will always give a thrust force; The blue arrow represents thrust force\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E \u003C\/p\u003E \u003Ch2\u003ESeparating action of Bevel gears\u003C\/h2\u003E\u003Cp\u003EYou can note that spider and side gear are bevel gears. It has got one specialty.  When torque is transmitted through a bevel gear system axial forces are also induced apart from the tangential force. The axial force tries to separate out the gears. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-iSqHz8ui4nI\/U3yKnLMm_NI\/AAAAAAAADDw\/e6dfXAMldlI\/s1600\/bevel+gear+action.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.5 During power transmission through a bevel gear system axial forces are also induced\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E You can note that side gear and axle are 2 separate units. The side gear has got a small allowance for axial movement. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/4.bp.blogspot.com\/-O2dVLF-5HbQ\/U3yKte0h5OI\/AAAAAAAADEg\/wlDFxT6JuA8\/s1600\/side_spider_gear+axle.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.6 Side gear and axle are two separate units as shown; So the side gear can have small axial movement\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E  So during high torque transmission through spider-side gear arrangement, a high separating thrust force is also transmitted to the clutch pack.  This force presses and locks the clutch pack assembly against wall of the casing.\u003C\/p\u003E   \u003Ch2\u003EWorking of Limited Slip Differential\u003C\/h2\u003E\u003Cp\u003ENow back to the initial problem.  Since one wheel is on a high traction surface, the torque transmitted to it will be higher. So the thrust force developed due to the bevel gear separation action also will be high at that side. Thus clutch pack at high traction wheel side will be pressed firmly and clutch pack will be locked.  So power from the differential casing will flow directly to high traction axle via clutch pack assembly.   \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-Ixfu9l7Jamg\/U3yKqMPeMfI\/AAAAAAAADEI\/d7ahqARbhqc\/s1600\/high+traction+power+flow.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.7 Thrust force induced due to the bevel gear separation action is high for the high traction wheel\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E  On the other hand clutch pack on the low traction wheel side is not engaged yet, so power flow will be limited to that side. So the vehicle will be able to overcome the traction difference problem.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-5HXQfWs21w0\/U3yKrxjgRDI\/AAAAAAAADEY\/lNtdm0eXRC0\/s1600\/right_clutch.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.8 Low thrust force at low traction wheel will allow steel plate and friction disc to slip\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E  \u003Cp\u003EHowever while taking a turn the LSD can act like a normal differential.  In this case thrust force developed due to bevel gear separation action won’t be that high. So the plates in clutch pack will easily overcome frictional resistance and will be able to slip against each other. Thus the right and left wheel can have different speed just like an open differential.\u003C\/p\u003E  \u003Cp\u003EFollowing are the other commonly used technologies used to overcome the drive wheel traction difference problem. \u003Cul\u003E\u003Cli\u003EClutch pack - Pressure disk type\u003C\/li\u003E\u003Cli\u003ETorsen\u003Csup\u003E®\u003C\/sup\u003E\u003C\/li\u003E\u003Cli\u003ECone Differential\u003C\/li\u003E\u003Cli\u003EHydraulic Locking Type\u003C\/li\u003E\u003C\/ul\u003E \u003C\/p\u003E \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/8219067920659538249"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/8219067920659538249"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2014\/05\/limited-slip-differential.html","title":"Working of a Limited Slip Differential "}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"https:\/\/1.bp.blogspot.com\/-CIho-qj6660\/U3yKuMvd6rI\/AAAAAAAADEo\/FJSlPwuRzR4\/s72-c\/traction+difference+problem.jpg","height":"72","width":"72"}},{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-2921013596763401544"},"published":{"$t":"2014-05-06T22:35:00.000-07:00"},"updated":{"$t":"2016-04-28T01:23:05.749-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Automobile"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Mechanics"}],"title":{"type":"text","$t":"How does a Differential work ?"},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cp\u003EThe differential is an integral part of all four wheelers. Differential technology was invented centuries ago and is considered to be one of the most ingenious inventions human thinking has ever produced. In this video, we will learn, in a logical manner, why a differential is needed in an automobile and its inner workings.   \u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe width=\"640\" height=\"360\" src=\"\/\/www.youtube.com\/embed\/SOgoejxzF8c\" frameborder=\"0\" allowfullscreen\u003E\u003C\/iframe\u003E\u003C\/div\u003E A detailed webpage version of the video lecture is given below.\u003C\/p\u003E\u003Chr\u003E\u003Cbr\u003E\u003Ch2\u003EWhy the Differential gear is used?\u003C\/h2\u003E\u003Cp\u003E Wheels receive power from the engine via a drive shaft. The wheels that receive power and make the vehicle move forward are called the drive wheels. The main function of the differential gear is to allow the drive wheels to turn at different rpms while both receiving power from the engine.\u003C\/p\u003E \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/3.bp.blogspot.com\/-UTPTV02kUiQ\/U2jHft4BwEI\/AAAAAAAADB8\/2yl7rD-KHks\/s1600\/power_flow_automobile.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.1 Power from the engine is flowed to the wheels via a drive shaft\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E \u003Cp\u003EConsider these wheels, which are negotiating a turn. It is clear that the left wheel has to travel a greater distance compared to the right wheel. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"Wheels taking right turn\" src=\"https:\/\/1.bp.blogspot.com\/-HvWy63-NOj0\/U2jHizBV9GI\/AAAAAAAADC0\/QD_sS9BB5Ew\/s1600\/wheels_taking_turn.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.2 While taking a right turn the left wheel has to travel more distance; this means more speed to left wheel\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E  This means that the left wheel has to rotate at a higher speed compared to the right wheel. If these wheels were connected using a solid shaft, the wheels would have to slip to accomplish the turn. This is exactly where a differential comes in handy. The ingenious mechanism in a differential allows the left and right wheels to turn at different rpms, while transferring power to both wheels.\u003C\/p\u003E \u003Ch2\u003EParts of a Differential\u003C\/h2\u003E\u003Cp\u003EWe will now learn how the differential achieves this in a step-by-step manner using the simplest configuration. Power from the engine is transferred to the ring gear through a pinion gear. The ring gear is connected to a spider gear.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"spider and ring gear\" src=\"https:\/\/4.bp.blogspot.com\/-De97CjRCAJY\/U2jHgT-xeqI\/AAAAAAAADCQ\/-B7fF_GTcR4\/s1600\/spider_gear_ring0300.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.3 Motion from the pinion gear is transferred to the spider gear\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E   The spider gear lies at the heart of the differential, and special mention should be made about its rotation. The spider gear is free to make 2 kinds of rotations: one along with the ring gear (\u003Ci\u003Erotation\u003C\/i\u003E) and the second on its own axis (\u003Ci\u003Espin\u003C\/i\u003E). \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"motion of spider gear\" src=\"https:\/\/1.bp.blogspot.com\/-O-WQ0RC8qew\/U2jHgCFcdEI\/AAAAAAAADCI\/gN2sCICx0Bc\/s1600\/spider_gear_motion.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.4 Spider gear is free to make 2 kinds of rotations\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E    The spider gear is meshed with 2 side gears. You can see that both the spider and side gears are bevel gears. Power flow from the drive shaft to the drive wheels follows the following pattern. From the drive shaft power is transferred to the pinion gear first, and since the pinion and ring gear are meshed, power flows to the ring gear. As the spider gear is connected with the ring gear, power flows to it. Finally from the spider gear, power gets transferred to both the side gears.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"the complete differential\" src=\"https:\/\/2.bp.blogspot.com\/-BNORZhRbpwk\/U2jHeCxoEcI\/AAAAAAAADBs\/cVqcOng7Jxw\/s1600\/full_differential.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.5 The basic components of a standard differential\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E \u003Cp\u003E   \u003Ch2\u003EDifferential Operation\u003C\/h2\u003E \u003Cp\u003ENow let’s see how the differential manages to rotate the side gears (drive wheels) at different speeds as demanded by different driving scenarios. \u003Ch3\u003E The vehicle moves straight\u003C\/h3\u003E\u003Cp\u003EIn this case, the spider gear rotates along with the ring gear but does not rotate on its own axis. So the spider gear will push and make both the side gears turn, and both will turn at the same speed. In short, when the vehicle moves straight, the spider-side gear assembly will move as a single solid unit.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"differential when vehicle moves straight\" src=\"https:\/\/3.bp.blogspot.com\/-XNUT6Rc2Njg\/U2jHhfPhYwI\/AAAAAAAADCc\/j7gNxWaGGhc\/s1600\/vehicle_moves_straight.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.6 While the vehicle moves straight, the spider gear does not spin; it pushes and rotate the side gears\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E \u003Ch3\u003EThe vehicle takes a right turn\u003C\/h3\u003E\u003Cp\u003ENow consider the case when the vehicle is taking a right turn. The spider gear plays a pivotal role in this case. Along with the rotation of the ring gear it rotates on its own axis. So, the spider gear is has a combined rotation. The effect of the combined rotation on the side gear is interesting.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"differential when vehicle turns right\" src=\"https:\/\/1.bp.blogspot.com\/-ZMkIP4NCvuM\/VGwl31z9wvI\/AAAAAAAADU4\/rNDBZYpn0m8\/s1600\/Vehicle_takes_right_turn.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.7 To get peripheral velocity at left and right side of spider gear we have to consider both rotation and spin of it\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E When properly meshed, the side gear has to have the same peripheral velocity as the spider gear. Technically speaking, both gears should have the same pitch line velocity. When the spider gear is spinning as well as rotating, peripheral velocity on the left side of spider gear is the sum of the spinning and rotational velocities. But on the right side, it is the difference of the two, since the spin velocity is in the opposite direction on this side. This fact is clearly depicted in Fig.7. This means the left side gear will have higher speed compared to the right side gear. This is the way the differential manages to turn left and right wheels at different speeds.\u003C\/p\u003E  \u003Ch3\u003EThe vehicle takes a left turn\u003C\/h3\u003E\u003Cp\u003EWhile taking a left turn, the right wheel should rotate at a higher speed. By comparing with the previous case, it is clear that, if the spider gear spins in the opposite direction, the right side gear will have a higher speed.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"differential when vehicle turns left\" src=\"https:\/\/1.bp.blogspot.com\/-rG__eoOrTk0\/VGwl35317bI\/AAAAAAAADU8\/AlqKq5a-Nqg\/s1600\/opposite_spider.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.8 While taking left turn the spider gear spins in opposite direction\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E\u003C\/p\u003E \u003Ch2\u003EUse of more Spider gears\u003C\/h2\u003E\u003Cp\u003EIn order to carry a greater load, one more spider gear is usually added. Note that the spider gears should spin in opposite directions to have the proper gear motion. A four-spider-gear arrangement is also used for vehicles with heavy loads. In such cases, the spider gears are connected to ends of a cross bar, and the spider gears are free to spin independently. \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"use of two spider gears\" src=\"https:\/\/2.bp.blogspot.com\/-1wZXr85hWm4\/VGwl31Eje-I\/AAAAAAAADU0\/ZJMjMhETWOs\/s1600\/double_spider_differential.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.9 Double spider gear arrangement is usually used to carry more loads\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E\u003C\/p\u003E\u003Ch2\u003EOther functions of the Differential\u003C\/h2\u003E  \u003Cp\u003EApart from allowing the wheels to rotate at different rpm differential has 2 more functions. First is speed reduction at the pinion-ring gear assembly. This is achieved by using a ring gear which is having almost 4 to 5 times number of teeth as that of the pinion gear. Such huge gear ratio will bring down the speed of the ring gear in the same ratio. Since the power flow at the pinion and ring gear are the same, such a speed reduction will result in a high torque multiplication.\u003C\/p\u003E\u003Cp\u003EYou can also note one specialty of the ring gear, they are hypoid gears. The hypoid gears have  more contact area compared to the other gear pairs and will make sure that the gear operation is smooth.\u003C\/p\u003E \u003Cp\u003EThe other function of the differential is to turn the power flow direction by 90 degree. \u003C\/p\u003E\u003Ch2\u003EDrawback of a Standard Differential\u003C\/h2\u003E\u003Cp\u003EThe differential we have gone through so far is known as \u003Ci\u003Eopen\u003C\/i\u003E or \u003Ci\u003Estandard differential\u003C\/i\u003E.  It is capable of turning the wheels at different rpm, but it has got one major drawback. Consider a situation where one wheel of the vehicle is on a surface with good traction and the other wheel on a slippery track.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"wheels on different traction\" src=\"https:\/\/2.bp.blogspot.com\/-M8ERDoWMVLo\/U2jQtuTVtGI\/AAAAAAAADDM\/AUE9BWX0xxQ\/s1600\/tranction_difference_differential.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.10 A standard differential vehicle on different traction surfaces will not be able to move\u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E  In this case a standard differential will send the majority of the power to the slippery wheel, so the vehicle won’t be able to move.  To overcome this problem, Limited Slip Differentials are introduced. We will learn more about them in a separate article. \u003C\/p\u003E \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/2921013596763401544"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/2921013596763401544"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2014\/05\/working-of-differential.html","title":"How does a Differential work ?"}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"https:\/\/3.bp.blogspot.com\/-UTPTV02kUiQ\/U2jHft4BwEI\/AAAAAAAADB8\/2yl7rD-KHks\/s72-c\/power_flow_automobile.jpg","height":"72","width":"72"}},{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-2545595709834527143"},"published":{"$t":"2013-08-24T19:15:00.001-07:00"},"updated":{"$t":"2016-04-28T01:27:19.203-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"}],"title":{"type":"text","$t":"Velocity Analysis | Mechanics"},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cp\u003ETo execute proper design of a mechanism, velocity analysis is of utmost importance.  A designer’s real interest in development of mechanism is variation of outlet link velocity for a specified inlet velocity. \u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe width=\"640\" height=\"360\" src=\"\/\/www.youtube.com\/embed\/jzNik6PEKG8\"  frameborder=\"0\" allowfullscreen\u003E\u003C\/iframe\u003E\u003C\/div\u003ECheck following article for detailed description of video lecture.\u003C\/p\u003E\u003Chr\u003E\u003Cbr\u003E\u003Cp\u003EThe interesting thing about velocity analysis is that, you can determine velocity of any link just by understanding 2 simple concepts.\u003C\/p\u003E\u003Col\u003E\u003Ch2\u003E\u003Cli\u003EConcept of Rigid Body\u003C\/li\u003E\u003C\/h2\u003E\u003Cp\u003E A rigid body cannot elongate or contract in any direction. That means if you take 2 points in a rigid body, it can have 2 different velocities as shown. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh5.googleusercontent.com\/-YAVVi5-HZmM\/Uhg6EhWSjPI\/AAAAAAAACoE\/WgHWKICDe9w\/s1600\/rigid_body.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh5.googleusercontent.com\/-YAVVi5-HZmM\/Uhg6EhWSjPI\/AAAAAAAACoE\/WgHWKICDe9w\/s1600\/rigid_body.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.1 2 points in a rigid body can have different velocities\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E But since this is rigid body, velocity components parallel to the line connecting the points should be equal. If component velocity of point B is greater than A, then link will start elongating. If the case is opposite link will start contracting. Both these cases are impossible, since this is a rigid body. So velocity components of both points should be equal. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh3.googleusercontent.com\/-ohD2fXaTeeA\/Uhg6fCUWIiI\/AAAAAAAACoc\/rUyYO66iA2U\/s1600\/rigid_body_velocity_components.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh3.googleusercontent.com\/-ohD2fXaTeeA\/Uhg6fCUWIiI\/AAAAAAAACoc\/rUyYO66iA2U\/s1600\/rigid_body_velocity_components.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.2 Velocity components of the points along the connecting line should be equal\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E  This means, if we subtract velocity of A from velocity of B, the relative velocity vector will have no component, parallel to the connecting line. It will get cancelled. So relative velocity vector will be perpendicular to the connecting line. This is shown in following figure.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh5.googleusercontent.com\/-UPyXvEDQuyE\/UhiS8B1cpLI\/AAAAAAAACpM\/dcq3LIyOKYI\/s1600\/relative_velocity_perpendicular.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh5.googleusercontent.com\/-UPyXvEDQuyE\/UhiS8B1cpLI\/AAAAAAAACpM\/dcq3LIyOKYI\/s1600\/relative_velocity_perpendicular.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.3 In a rigid body relative velocity vector should be perpendicular to line connecting themr\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E In short, concept 1 can be simplified as, relative velocity between any 2 points in a rigid body should be perpendicular to the line connecting them.\u003C\/p\u003E\u003Ch2\u003E\u003Cli\u003ENo Penetration of Mating Surfaces\u003C\/li\u003E\u003C\/h2\u003E\u003Cp\u003ESecond concept is applicable to mating surfaces. Mating pair of surface will never penetrate. Red point in folloiwng figure shows the common mating point or mating line for both the links. Common normal of the mating surfaces is also shown. The same point can have different velocities on different links.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh3.googleusercontent.com\/-9e_a_9fbFLs\/UhiS2Rv55iI\/AAAAAAAACpE\/MEPG-UtqYqk\/s1600\/mating_surfaces.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh3.googleusercontent.com\/-9e_a_9fbFLs\/UhiS2Rv55iI\/AAAAAAAACpE\/MEPG-UtqYqk\/s1600\/mating_surfaces.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.4 Mating point is having different velocities on different links\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E No penetration means velocity component of both the link velocities along common normal should be equal. If velocity component of 2 is less than velocity component of 1, then surfaces will penetrate. If opposite is the case, surfaces will detach. Both these cases are not possible for mating surfaces. So velocity components along common normal should be equal.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh3.googleusercontent.com\/-Z3zwspt9Nk8\/UhiSiLJGPRI\/AAAAAAAACo0\/OQ6TyOW1H8A\/s1600\/mating_surfaces_relative%2520velocities.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh3.googleusercontent.com\/-Z3zwspt9Nk8\/UhiSiLJGPRI\/AAAAAAAACo0\/OQ6TyOW1H8A\/s1600\/mating_surfaces_relative%2520velocities.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.5 Relative velocity vector of mating point should be perpendicular to common normal\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E  Since velocity components are equal, if we take a vector difference of V 1 and V 2, it should have no component along the common normal. So the relative velocity should be perpendicular to common normal.\u003C\/p\u003E\u003C\/ol\u003E \u003Cp\u003ENow we will apply these 2 concepts on different mechanisms, to do velocity analysis of them.\u003C\/p\u003E\u003Ch2\u003E 4 Bar Linkage Example\u003C\/h2\u003E\u003Cp\u003ELet's consider 4 bar linkage shown below. We know input angular velocity and we want to find out outlet velocity.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh5.googleusercontent.com\/-zB52UFkr49k\/Uhip2oaOYyI\/AAAAAAAACpg\/D19olph10dQ\/s1600\/4Bar_linkage.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh5.googleusercontent.com\/-zB52UFkr49k\/Uhip2oaOYyI\/AAAAAAAACpg\/D19olph10dQ\/s1600\/4Bar_linkage.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.6 Example of 4 bar linkage\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E  Here approach is simple. We will say that bar at middle cannot expand or contract. Since we know angular velocity of first link, we can easily find out magnitude and direction of velocity of point 1.But for point 2 we know only direction of velocity. Here first concept we learned comes for help. Since this bar cannot elongate or contract, relative velocity between these points should be perpendicular to this link.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh6.googleusercontent.com\/-zoj5RG_NnTk\/Uhg6qLHJQDI\/AAAAAAAACok\/hzrDm20RmDM\/s1600\/4_bar_linkage_solution.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh6.googleusercontent.com\/-zoj5RG_NnTk\/Uhg6qLHJQDI\/AAAAAAAACok\/hzrDm20RmDM\/s1600\/4_bar_linkage_solution.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.7 Procedure of 4 bar linkage\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E  Which will lead to, magnitude of velocity at point 2. From here angular velocity of link can easily be deduced.\u003C\/p\u003E\u003Ch2\u003E Cam-Cam Example\u003C\/h2\u003E\u003Cp\u003ENow consider this mechanism. We know angular velocity of first cam, we want to find out angular velocity of the second cam.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh6.googleusercontent.com\/-ucUSMqMJ3BU\/Uhg6NphvIkI\/AAAAAAAACoM\/DpgNojDMi3I\/s1600\/cam_cam_example.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh6.googleusercontent.com\/-ucUSMqMJ3BU\/Uhg6NphvIkI\/AAAAAAAACoM\/DpgNojDMi3I\/s1600\/cam_cam_example.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.8 Example of cam cam mechanism\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E  Common normal at the time of mating is marked in figure. Consider the mating point, which lies on both the cams. We know velocity direction and magnitude of this point on first cam. But for second cam we know only direction. The direction is marked in figure.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh5.googleusercontent.com\/-ZSRXXSvpKUQ\/UhiSmosmkmI\/AAAAAAAACo8\/08BqyNxzl1I\/s1600\/common_normal_v2_cam_cam.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh5.googleusercontent.com\/-ZSRXXSvpKUQ\/UhiSmosmkmI\/AAAAAAAACo8\/08BqyNxzl1I\/s1600\/common_normal_v2_cam_cam.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.1 Mains parts of single phase induction motor : Rotor and Stator\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E  Here 2nd concept we learned comes to help. Since the links cannot penetrate, relative velocity should be perpendicular to common normal. So we can find out magnitude of V\u003Csub\u003E2\u003C\/sub\u003E, which will lead to link angular velocity.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh4.googleusercontent.com\/-Grv1oHkqYSU\/Uhg6bee2ZII\/AAAAAAAACoU\/p5te6nADIFA\/s1600\/solution_cam_cam.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/lh4.googleusercontent.com\/-Grv1oHkqYSU\/Uhg6bee2ZII\/AAAAAAAACoU\/p5te6nADIFA\/s1600\/solution_cam_cam.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.1 Mains parts of single phase induction motor : Rotor and Stator\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003C\/p\u003E \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/2545595709834527143"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/2545595709834527143"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2013\/08\/velocity-analysis-mechanics.html","title":"Velocity Analysis | Mechanics"}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"https:\/\/lh5.googleusercontent.com\/-YAVVi5-HZmM\/Uhg6EhWSjPI\/AAAAAAAACoE\/WgHWKICDe9w\/s72-c\/rigid_body.jpg","height":"72","width":"72"}},{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-6232785721672319939"},"published":{"$t":"2013-04-18T02:23:00.001-07:00"},"updated":{"$t":"2016-04-28T01:29:11.822-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Mechanics"}],"title":{"type":"text","$t":"Understanding Degrees of Freedom "},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cp\u003EDegrees of freedom is the one of the most important concept in mechanics. This concept is widely used in robotics and kinematics. D.O.F means how many variables are required to determine position of a mechanism in space. In this video lecture we will understand how to predict degrees of freedom of a mechanism. \u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe width=\"640\" height=\"360\" src=\"http:\/\/www.youtube.com\/embed\/vOFM8eG8kVc\" frameborder=\"0\" allowfullscreen\u003E\u003C\/iframe\u003E\u003C\/div\u003EDetailed description of the video lecture is given below.\u003C\/p\u003E\u003Chr\u003E\u003Cbr\u003E\u003Ch2\u003E Degrees of Freedom – Examples\u003C\/h2\u003E\u003Cp\u003EConsider the mechanism shown in first figure of Fig.4. Position of this 4 bar mechanism can be completely determined just by knowing angle or position of any  one of the member. So degree of freedom is one. Similarly degree of freedom of the cam and follower mechanism is also one. But to determine position of the slider crank mechanism shown, we should know angle or displacement of at least 2 members. So here degrees of  freedom is 2.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-4MWAjpQP-D4\/UWZy_0nbwgI\/AAAAAAAABmE\/RRGwQwRxqFw\/s1600\/cmparing+Degrees+of+freedom.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-4MWAjpQP-D4\/UWZy_0nbwgI\/AAAAAAAABmE\/RRGwQwRxqFw\/s1600\/cmparing+Degrees+of+freedom.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.1 Examples of degrees of freedom of different mechanisms\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EYou have predicted D.O.F of some simple mechanisms from your intuition. But for a complex mechanism, such an approach may not work. So  in coming sections we will  see how we can predict D.O.F of a mechanism.\u003C\/p\u003E \u003Ch2\u003E Degrees of Freedom of a Rigid Body\u003C\/h2\u003E\u003Cp\u003EConsider the rigid body shown below, which is situated in space. It could have 3 translatory motions as shown. Also it could have 3 rotary motions as shown.In total we need 6 inputs to determine its position. So degree of freedom of rigid body in space is 6.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-tvTJo-rTKV0\/UWZy8-ow1gI\/AAAAAAAABlg\/6t86oZAHOO0\/s1600\/3+dimensional+mobility.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/2.bp.blogspot.com\/-tvTJo-rTKV0\/UWZy8-ow1gI\/AAAAAAAABlg\/6t86oZAHOO0\/s1600\/3+dimensional+mobility.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.2 A rigid body in space can have total 6 degrees of freedom\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EIf the body is in a plane it can have only 3 motions. 2 translational and 1 rotational. So degree of freedom of a rigid body in a plane is 3. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-4JZaUKvvOr4\/UWZzBnk0XiI\/AAAAAAAABmc\/1akVGjTqbX0\/s1600\/planar+mobility.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-4JZaUKvvOr4\/UWZzBnk0XiI\/AAAAAAAABmc\/1akVGjTqbX0\/s1600\/planar+mobility.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.3 A rigid body on plane can have total 3 degrees of freedom\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003C\/p\u003E\u003Ch2\u003EDegrees of Freedom of a Mechanism\u003C\/h2\u003E\u003Cp\u003EA mechanism is a collection of rigid bodies or links, connected through pairs, provided one link is grounded. Consider the mechanism shown below. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-Y12MWmM1OcQ\/UW0pqv1m-OI\/AAAAAAAABnI\/F3LzKgiCR8I\/s1600\/planar_mechanism.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-Y12MWmM1OcQ\/UW0pqv1m-OI\/AAAAAAAABnI\/F3LzKgiCR8I\/s320\/planar_mechanism.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.4 An example of mechanism, it is necessary that one link should be groudnded\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EIf this system were not connected like this, then each link except the ground would have 3 degrees of freedom.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-Q5HG0rIYVZk\/UWZzAs6bOxI\/AAAAAAAABmQ\/KJp_r3uG1PI\/s1600\/dis+assembled+mechanism.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/4.bp.blogspot.com\/-Q5HG0rIYVZk\/UWZzAs6bOxI\/AAAAAAAABmQ\/KJp_r3uG1PI\/s1600\/dis+assembled+mechanism.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.5 If links were not connected each link would have 3 D.O.F, except the ground\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003ESo total degrees of freedom, or mobility is \u003Ci\u003E3(N-1)\u003C\/i\u003E. \u003Ci\u003EN\u003C\/i\u003E represents total number of links. In this case \u003Ci\u003EN\u003C\/i\u003E is 3. But when we connect it together through pairs, links will not have the same 3 degrees of freedom.\u003C\/p\u003E\u003Cp\u003EIf joint between 2 links is having surface contact as shown below, then both the links will have same translatory motion, in X and Y directions.So for each such pairs, there will be a deduction of 2 mobility from total mobility. Where \u003Ci\u003EL\u003Csub\u003EP\u003C\/sub\u003E\u003C\/i\u003E represents number of pairs with surface contacts. Such pairs are called lower pairs. In this case we have 2 lower pairs.\u003C\/p\u003E\u003Cp\u003ENow consider the joint which is having a line contact. If joint between 2 links is having line or point contact, both the link should have same translational motion along the common normal. However it could have different motion, in tangential direction. So for each such pairs, there will be deduction of 1 mobility from total mobility. This kind of pair is called higher pair. Here we have got 1 higher pair.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-FyjRLTYlz0c\/UWZzApms7AI\/AAAAAAAABmU\/QdeAq_egnTI\/s1600\/pairs_in+mechanism.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-FyjRLTYlz0c\/UWZzApms7AI\/AAAAAAAABmU\/QdeAq_egnTI\/s1600\/pairs_in+mechanism.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.6 Lower pairs and higher pairs in a mechanism, a lower pair arrests 2 D.O.F, while a higher pair arrests one D.O.F\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E So this mechanism has got 1 degree of freedom. Means, by knowing position of only one cam, we can completely determine this mechanism.\u003C\/p\u003E \u003Cp\u003EThe general equation to find out degrees of freedom of a planar mechanism is given below. This equation is also  known as \u003Ci\u003EKuthbach equation\u003C\/i\u003E. \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-5JcsK8n-SSA\/UW-4MgnKzBI\/AAAAAAAABnY\/_f5E_p1p4o4\/s1600\/mobility+equation+planar.GIF\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/4.bp.blogspot.com\/-5JcsK8n-SSA\/UW-4MgnKzBI\/AAAAAAAABnY\/_f5E_p1p4o4\/s1600\/mobility+equation+planar.GIF\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EHere \u003Ci\u003EN\u003C\/i\u003E represent total number of links in the mechanism. \u003Ci\u003EL\u003Csub\u003EP\u003C\/sub\u003E\u003C\/i\u003E and \u003Ci\u003EH\u003Csub\u003EP\u003C\/sub\u003E\u003C\/i\u003E represent number of lower pairs and higher pairs respectively.\u003C\/p\u003E\u003Ch3\u003E 4 Bar Linkage \u003C\/h3\u003E\u003Cp\u003EBack to same old planar mechanisms.This mechanism is having 4 links, and 4 lower pairs. So you can predict from \u003Ci\u003EKuthbach equation\u003C\/i\u003E that mobility of the mechanism is 1. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-Z5XSJTsPp8A\/UWZy9_2vEhI\/AAAAAAAABlw\/h5sg8fG-gUI\/s1600\/4+bar+linkage.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-Z5XSJTsPp8A\/UWZy9_2vEhI\/AAAAAAAABlw\/h5sg8fG-gUI\/s1600\/4+bar+linkage.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.7 4 bar linkage, it is having 4 links and 4 lower pairs\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003C\/p\u003E\u003Ch3\u003ECam and Follower \u003C\/h3\u003E\u003Cp\u003ECam and follower is having 3 links, 2 lower pairs, and one higher pair.So mobility is again one. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-veVL9w8IU9k\/UWZy-onr2fI\/AAAAAAAABmA\/m1p2F7QjwG0\/s1600\/Cam+and+Follower.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-veVL9w8IU9k\/UWZy-onr2fI\/AAAAAAAABmA\/m1p2F7QjwG0\/s1600\/Cam+and+Follower.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.8 Cam and follower, 3 links, 2 lower pairs, 1 higher pair\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003C\/p\u003E  \u003Ch3\u003E5 bar linkage\u003C\/h3\u003E\u003Cp\u003EThis mechanism is having 5 links and 5 lower pairs. So mobility is 2. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-MgyBWB-msis\/UWZy-jysQcI\/AAAAAAAABl8\/c6s5YdVySEY\/s1600\/5+bar+linkage.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/2.bp.blogspot.com\/-MgyBWB-msis\/UWZy-jysQcI\/AAAAAAAABl8\/c6s5YdVySEY\/s1600\/5+bar+linkage.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.9 5 bar linkage, 5 links, 5 lower pairs\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003C\/p\u003E \u003Ch2\u003EA 3 Dimensional Mechanism\u003C\/h2\u003E\u003Cp\u003EIf the mechanism is 3 dimensional in nature, you could easily derive an equation for mobility using the same concept. So equation for degree of freedom would be as follows  \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-gOqV58HxU7A\/UWZy88T9sgI\/AAAAAAAABlo\/Spc2SXDKDyA\/s1600\/3d_mobility_equation.png\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/2.bp.blogspot.com\/-gOqV58HxU7A\/UWZy88T9sgI\/AAAAAAAABlo\/Spc2SXDKDyA\/s1600\/3d_mobility_equation.png\" \/\u003E\u003C\/a\u003E\u003C\/div\u003E  Where \u003Ci\u003EP\u003Csub\u003En\u003C\/sub\u003E\u003C\/i\u003E represents number of pairs which block \u003Ci\u003E'n'\u003C\/i\u003E degrees of freedom. The main thing here will be determination of nature of pair. You can use this equation to predict D.O.F following 3 dimensional mechanism. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-piwncg1pRDg\/UWZy88GFl3I\/AAAAAAAABlk\/hOwk78T4aiI\/s1600\/3+dimensional+mechanism.jpg\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/2.bp.blogspot.com\/-piwncg1pRDg\/UWZy88GFl3I\/AAAAAAAABlk\/hOwk78T4aiI\/s1600\/3+dimensional+mechanism.jpg\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.10 A 3 dimensional mechansim\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003C\/p\u003E \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/6232785721672319939"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/6232785721672319939"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2013\/04\/degrees-of-freedom-mechanics.html","title":"Understanding Degrees of Freedom "}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"https:\/\/img.youtube.com\/vi\/vOFM8eG8kVc\/default.jpg","height":"72","width":"72"}},{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-6837705395696422733"},"published":{"$t":"2013-03-12T02:40:00.001-07:00"},"updated":{"$t":"2016-04-28T01:28:20.513-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Structural"}],"title":{"type":"text","$t":"Fatigue Failure Analysis"},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cp\u003EEven if you design mechanical components satisfying mechanical strength criteria it may fail due to a phenomenon called fatigue. Historically many design disasters have happened by neglecting effect of Fatigue.In this video lecture we will learn how to predict and quantify fatigue effect.\u003C\/p\u003E\u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe width=\"640\" height=\"360\" src=\"http:\/\/www.youtube.com\/embed\/ywDsB3umK2Y\" frameborder=\"0\" allowfullscreen\u003E\u003C\/iframe\u003E\u003C\/div\u003E\u003Cp\u003EDetailed description of above video lecture is given below\u003C\/p\u003E\u003Chr\u003E\u003Ch2\u003EA Wire Breaking problem\u003C\/h2\u003E\u003Cp\u003ETo understand what is fatigue let’s consider this metal wire. You have to break it. So how will you break it? Will you pull it from both ends or will you bend the wire upward and downward repetitively. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-J8wm63b3Iy0\/UT7pcuazyyI\/AAAAAAAABhg\/bZKe01svpVw\/s1600\/wire_breaking_methods.gif\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-J8wm63b3Iy0\/UT7pcuazyyI\/AAAAAAAABhg\/bZKe01svpVw\/s1600\/wire_breaking_methods.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.1 Two methods to break metal wire, Either bend it upward and downward repetitively or pull it\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EYour answer is obviously the second option. Because this method requires less effort compared to the first case. This is a well known example of fatigue failure. So how does material fail due to fatigue? To get answer for this question let us have a close look at stress variation in wire cross section.\u003C\/p\u003E\u003Ch2\u003EReason Behind Fatigue Failure - Crack Propagation \u003C\/h2\u003E\u003Cp\u003EWhen you bend it downwards bending stress induced is  in the wire cross section. There will be tension at top area and compression at bottom area. When wire is at equilibrium there will not be any stress on wire cross section. When wire is bending upwards there will be compression at top and tension at bottom.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-cJr8fY6o2vw\/UT7pa-aSzUI\/AAAAAAAABhI\/N2tKXxNRBNk\/s1600\/1_stress_variation_wire.gif\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/2.bp.blogspot.com\/-cJr8fY6o2vw\/UT7pa-aSzUI\/AAAAAAAABhI\/N2tKXxNRBNk\/s1600\/1_stress_variation_wire.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.2 Stress variation in wire cross-section, as wire is bent downward and upward\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003ESo if you trace stress induced at a point with respect to time it will vary like this. As a fluctuating stress with time. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-dF8-f8lRJJk\/UT7pawoxj8I\/AAAAAAAABhE\/yimwuLTA2R8\/s1600\/2_stress_vs_time.gif\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/2.bp.blogspot.com\/-dF8-f8lRJJk\/UT7pawoxj8I\/AAAAAAAABhE\/yimwuLTA2R8\/s1600\/2_stress_vs_time.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.3 Stress variation at a point is plttod on stress vs time graph\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EInitially the point will have positive stress, after that zero, then negative stress. The same cycle repeats again and again. Such fluctuating stress is root cause of fatigue failure.  When such fluctuating load act on a material it will initiate something called micro crack. This crack will begin to grow with fluctuating load and over time it will cause an abrupt failure.  Unlike failure due to static load failure due to fatigue happens without any warning, it does not make necking. And the failure is unpredictable.\u003C\/p\u003E\u003Ch2\u003EFatigue Failure in Real Life Engineering Problems\u003C\/h2\u003E\u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-jarD5Sgit4M\/UT7pcbcUElI\/AAAAAAAABhc\/Sp33mZX2JW0\/s1600\/motor_gear_fatigue_failure.gif\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/2.bp.blogspot.com\/-jarD5Sgit4M\/UT7pcbcUElI\/AAAAAAAABhc\/Sp33mZX2JW0\/s1600\/motor_gear_fatigue_failure.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.4 Some practical cases which could result in fatigue failure, if not designed properly\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E   \u003Cp\u003EThe same phenomenon can happen for axle of this motor where it  is undergoing fluctuating stress due to gravity effect of this mass.  A rail wheel when it is in contact with with the track produces a high contact stress, but when the wheel rotates stress gets relieved. When it comes back to original position again contact stress arises. So this also is a case of fluctuating stress case. Again will lead to fatigue failure if we do not design it carefully.  Same is the case with a gear pair. Here contact stress arised at contact point fluctuates with time.\u003C\/p\u003E\u003Ch2\u003EEffect of Stress Amplitude on Number of Cycles - S N Curve\u003C\/h2\u003E\u003Cp\u003EThis is the most important part in fatigue analysis. Relationship between stress amplitude and number of cycles it can execute before it fails. As you can guess as stress amplitude increases number of cycles for failure decreases.  We will draw number of cycles in x axis, Stress amplitude in y axis. Both in logarithmic scale.  Let’s start with the maximum stress a material can withstand, its ultimate stress. So this will happen, as you increase the stress even before completing one cycle the material will get broken.  If you decrease the stress amplitude it will execute more number of cycles before it fails. Decreasing stress further even more number of cycles. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-BoHL8w0kdJg\/UT7pa3Q9aEI\/AAAAAAAABhA\/xp041nVoBqg\/s1600\/3_stress_number_of_cycles.gif\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/4.bp.blogspot.com\/-BoHL8w0kdJg\/UT7pa3Q9aEI\/AAAAAAAABhA\/xp041nVoBqg\/s1600\/3_stress_number_of_cycles.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.5 Number of cylces for fatigue failure increases with decrease in stress amplitude \u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003ESo this will follow a trend like this, but not forever. You can see after particular stress amplitude, even with slight decrease in stress number of cycles required to make it fail increases drastically. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-VIJ5JNtlwcU\/UT7pbpeeEBI\/AAAAAAAABhQ\/HhgVe-Q5W9s\/s1600\/4_SN_Curve.gif\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/2.bp.blogspot.com\/-VIJ5JNtlwcU\/UT7pbpeeEBI\/AAAAAAAABhQ\/HhgVe-Q5W9s\/s1600\/4_SN_Curve.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.6 Stress amplitude Vs number of cycles, green region represents safe design area\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EOr in short if you have stress amplitude below this limit number of cycles to make to fail jumps ton infinity. Or material never fails after this limit.  the material never fails.  This limit is known as endurance limit; below endurance limit it is safe to operate the material. Engineers always try to design their components by keeping stress amplitude below endurance limit. You can see that endurance limit is way below ultimate stress value.\u003C\/p\u003E\u003Ch2\u003EFatigue Failure, when there is no Complete Stress Reversal\u003C\/h2\u003E\u003Cp\u003EThe case we discussed had complete stress reversal. What will be maximum stress limit for this case ?. When stress reversal does not happen. It has got a mean value and amplitude. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-0Bp-B8ur9ts\/UT7pcHJawnI\/AAAAAAAABhY\/XmLwxP6Ro_s\/s1600\/Stress_cycle_mean_value.gif\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-0Bp-B8ur9ts\/UT7pcHJawnI\/AAAAAAAABhY\/XmLwxP6Ro_s\/s1600\/Stress_cycle_mean_value.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.7 Fluctuating stress case which is not fully reversed\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EFor this purpose we have to use something called Goodman diagram.  Where mean value of stress is drawn on x axis. Amplitude of stress is drawn on y axis. When mean value of zero, we know safe stress limit is same as endurance limit.  When amplitude of stress is zero, it is same as a static loading condition. So safe limit for tension is ultimate tensile stress at tension and safe limit for compression is ultimate tensile stress for compression. According to Goodman analysis safe stress amplitude limits for other cases lie on straight lines connecting this points. So for a particular stress mean value, we can find what’s the maximum allowable safe stress limit from this diagram. It will be here. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-6fO_fX4yxYg\/UT7pbqUMNtI\/AAAAAAAABhU\/kq8iAvimCS4\/s1600\/5_Goodman_diagram.gif\" imageanchor=\"1\" \u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-6fO_fX4yxYg\/UT7pbqUMNtI\/AAAAAAAABhU\/kq8iAvimCS4\/s1600\/5_Goodman_diagram.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.8 Use of Goodman diagram to find safe stress amplitude when stresmm mean value is not zero\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003ESimilar analysis can be done considering, safe limit of amplitude zero condition as yield strength of material. This is known as Soberberg diagram.  Generally Goodman analysis is the most preferred one.\u003C\/p\u003E \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/6837705395696422733"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/6837705395696422733"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2013\/03\/fatigue-failure-analyis.html","title":"Fatigue Failure Analysis"}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"https:\/\/img.youtube.com\/vi\/ywDsB3umK2Y\/default.jpg","height":"72","width":"72"}},{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-8784643573168582911"},"published":{"$t":"2013-02-04T19:20:00.000-08:00"},"updated":{"$t":"2016-04-28T01:15:32.316-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"}],"title":{"type":"text","$t":"Spur Gear Design"},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cp\u003EMechanical engineers working in transmission field would often have to decide upon kind of gears they have to use. Although this task has become a matter of selection of gear based on standards, it is also important to know what goes behind this. In this video tutorial you will learn how to design a pair of spur gears for mechanical strength, surface resistance and fluctuating load. \u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe width=\"640\" height=\"360\" src=\"http:\/\/www.youtube.com\/embed\/8bml2pK6Ra0\" frameborder=\"0\" allowfullscreen\u003E\u003C\/iframe\u003E\u003C\/div\u003EThe video lecture is described below in detail\u003C\/p\u003E\u003Chr\u003E\u003Cbr\u003E\u003Ch2\u003EAGMA Standard of Gear Design\u003C\/h2\u003E\u003Cp\u003EA designed gear should meet following design criteria conforming to AGMA standards. It should have \u003Col\u003E\u003Cli\u003EEnough mechanical strength to withstand force transmitted\u003C\/li\u003E\u003Cli\u003EEnough surface resistance to overcome pitting failure\u003C\/li\u003E\u003Cli\u003EEnough dynamic resistance to carry fluctuating loads\u003C\/li\u003E\u003C\/ol\u003E\u003Ch2\u003EDesign Inputs and Outputs in Gear Design\u003C\/h2\u003E\u003Cp\u003EFollowing figure shows design inputs and outputs of a gear design \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-n7V8TCJDvVs\/UQ-S0QHlzVI\/AAAAAAAABJQ\/E7l8IZhhLiw\/s1600\/gear_design_input_output.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/4.bp.blogspot.com\/-n7V8TCJDvVs\/UQ-S0QHlzVI\/AAAAAAAABJQ\/E7l8IZhhLiw\/s1600\/gear_design_input_output.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.1 Input and output parameters for a gear design\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EVarious design output parameters are pictorially represented in following figure.\u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-JfT0OmW1UxU\/URBKSmr83nI\/AAAAAAAABLs\/cdoi5GQ2554\/s1600\/spur_gear_parameters.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/1.bp.blogspot.com\/-JfT0OmW1UxU\/URBKSmr83nI\/AAAAAAAABLs\/cdoi5GQ2554\/s1600\/spur_gear_parameters.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.2 A general spur gear nomenclatures\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003C\/p\u003E\u003Ch2\u003EDesign for space constrains\u003C\/h2\u003E\u003Cp\u003EThe designed gear system should fit within a space limit. So the designer could say if he sums pitch diameters of the mating gears, it should be less than or equal to allowable space limit as shown in figure below. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-JeFcLJjISUQ\/UQ-YwGUrpwI\/AAAAAAAABJ8\/Acgfh5-BAtI\/s1600\/2_gear_allowable_width.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/1.bp.blogspot.com\/-JeFcLJjISUQ\/UQ-YwGUrpwI\/AAAAAAAABJ8\/Acgfh5-BAtI\/s1600\/2_gear_allowable_width.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.3 Space constrain of gear design\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EThe blue rectangle represents space on which gear should get fit. One can take 80% of width of this space as allowable width for gear design. So following is the relation obtained by this condition. \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-0L6h3elkpRc\/URBgZT-eCAI\/AAAAAAAABNs\/Bjpd3RoRBa4\/s1600\/1.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/2.bp.blogspot.com\/-0L6h3elkpRc\/URBgZT-eCAI\/AAAAAAAABNs\/Bjpd3RoRBa4\/s1600\/1.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EWe also know speed ratio of gears, this will lead to one more relation in terms of pitch circle diameters.  \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-wGoxaZGdADM\/URBgaJ8IzPI\/AAAAAAAABN4\/AXiVkt8o1rU\/s1600\/2.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/3.bp.blogspot.com\/-wGoxaZGdADM\/URBgaJ8IzPI\/AAAAAAAABN4\/AXiVkt8o1rU\/s1600\/2.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EBy solving above 2 equations simultaneously we can obtain pitch circle diameters of both the gears. \u003C\/p\u003E\u003Ch2\u003EDetermination of Number of Teeth - Interference\u003C\/h2\u003E\u003Cp\u003EHere we will understand how to determine number of teeth on both the gears. To do this we have to assume number of teeth on one gear(T1), say the smaller gear. Now using the relation given below we can determine number of teeth on other gear,T2. \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/---CEgUx1608\/URBgayLqtVI\/AAAAAAAABOE\/udvxZ7PaO0E\/s1600\/3.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/4.bp.blogspot.com\/---CEgUx1608\/URBgayLqtVI\/AAAAAAAABOE\/udvxZ7PaO0E\/s1600\/3.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003E So we got number of teeth on both the gears, but one should also check for a phenomenon called interference if gear system has to have a smooth operation. Interference happens when gear teeth has got profile below base circle. This will result high noise and material removal problem. This phenomenon is shown in following figure. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-xVXlgy2HaAI\/UQ-Y2oQmCWI\/AAAAAAAABKI\/iX4aDPxFFNE\/s1600\/3_gear_interference.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/2.bp.blogspot.com\/-xVXlgy2HaAI\/UQ-Y2oQmCWI\/AAAAAAAABKI\/iX4aDPxFFNE\/s1600\/3_gear_interference.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.4 A pair of gear teeth under interference\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EIf one has to remove interference , the pinion should have a minimum number of teeth specified by following relation. \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/--yBZi2LWurk\/URBgbiCnTCI\/AAAAAAAABOQ\/TgC0OF9Ra00\/s1600\/4.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\" height=\"61\" width=\"181\" src=\"https:\/\/4.bp.blogspot.com\/--yBZi2LWurk\/URBgbiCnTCI\/AAAAAAAABOQ\/TgC0OF9Ra00\/s400\/4.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EWhere aw represents addendum of tooth. For 20 degree pressure angle(which is normally taken by designers) aw = 1 m and bw = 1.2 m. Module m, and pitch circle diameter Pd are defined as follows.\u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-l9d5VHoKPU0\/URBl4LNra9I\/AAAAAAAABP8\/BzCkXQF-PzE\/s1600\/10.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/2.bp.blogspot.com\/-l9d5VHoKPU0\/URBl4LNra9I\/AAAAAAAABP8\/BzCkXQF-PzE\/s1600\/10.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003E\u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-Lot7NpayWCE\/URBl4pfv6MI\/AAAAAAAABQI\/xHhxchs9vEQ\/s1600\/11.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/4.bp.blogspot.com\/-Lot7NpayWCE\/URBl4pfv6MI\/AAAAAAAABQI\/xHhxchs9vEQ\/s1600\/11.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EIf this relation does not hold for a given case, then one has to increase number of teeth T1, and redo the calculation. The algorithm for deciding number of teeth T1 and T2 is shown below.\u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-kbPRuzxAoZk\/UQ-Y2-xEJtI\/AAAAAAAABKU\/-Isn9mTleLw\/s1600\/4_gear_tooth_number_algorithm.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-kbPRuzxAoZk\/UQ-Y2-xEJtI\/AAAAAAAABKU\/-Isn9mTleLw\/s1600\/4_gear_tooth_number_algorithm.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.5 Flow chart to determine number of teeth on each gears\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003C\/p\u003E \u003Ch2\u003EDesign for Mechanical Strength - Lewis Equation\u003C\/h2\u003E\u003Cp\u003ENow the major parameter remaining in gear design is width of the gear teeth, b. This is determined by checking whether maximum bending stress induced by tangential component of transmitted load, Ft at the root of gear is greater than allowable stress. As we know power transmitted,P and pitch line velocity V of the gear Ft can be determined using following relation. \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-2NIzogdhVIw\/URBgcPvQEhI\/AAAAAAAABOc\/XoOU1-syeN0\/s1600\/5.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/3.bp.blogspot.com\/-2NIzogdhVIw\/URBgcPvQEhI\/AAAAAAAABOc\/XoOU1-syeN0\/s1600\/5.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EHere we consider gear tooth like a cantilever which is under static equilibrium. Gear forces and detailed geometry of the tooth is shown in figure below. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-lBOE2ed9zlc\/UQ-Z6ZFoHXI\/AAAAAAAABKk\/EGssaUqq7nc\/s1600\/5_gear_design_for_stregth_Lewis.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/3.bp.blogspot.com\/-lBOE2ed9zlc\/UQ-Z6ZFoHXI\/AAAAAAAABKk\/EGssaUqq7nc\/s1600\/5_gear_design_for_stregth_Lewis.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.6 Gear tooth under load\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EOne can easily find out maximum value of bending stress induced if all geometrical parameters shown in above figure are known. But the quantities t and l are not easy to determine, so we use an alternate approach to find out maximum bending stress value using Lewis approach. Maximum bending stress induced is given by Lewis bending equation as follows.\u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-p0lUirhRLkg\/URBgkFh5bhI\/AAAAAAAABOo\/1-tDDKWQXtk\/s1600\/6.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/4.bp.blogspot.com\/-p0lUirhRLkg\/URBgkFh5bhI\/AAAAAAAABOo\/1-tDDKWQXtk\/s1600\/6.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EWhere Y is Lewis form factor, which is a function of pressure angle, number of teeth and addendum and dedendum. Value of Y is available as in form of table or graph. Using above relation one can determine value of b, by substituting maximum allowable stress value of material in LHS of equation. But a gear design obtained so will be so unrealistic, because in this design we are considering gear tooth like a cantilever which is under static equilibrium. But that's not the actual case. In next session we will  incorporate  many other parameters which will affect mechanical strength of the gear in order to get more realistic design. \u003C\/p\u003E \u003Ch2\u003EA More Realistic Approach - AGMA Strength Equation\u003C\/h2\u003E\u003Cp\u003EWhen a pair of gear rotates we often hear noise from this, this is due to collision happening between gear teeth due to small clearance in between them. Such collisions will raise load on the gear more than the previously calculated value. This effect is incorporated in dynamic loading loading factor, Kv value of which is a function of pitch line velocity.\u003C\/p\u003E\u003Cp\u003EAt root of the gear there could be fatigue failure due to stress concentration effect. Effect of which is incorporated in a factor called Kf value of which is more than 1. \u003C\/p\u003E\u003Cp\u003EThere will be factors to check for overload (Ko) and load distribution on gear tooth (Km). While incorporating all these factors Lewis stregth equation will be modified like this \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-cVWKVNbr2Vc\/URBgka9iCUI\/AAAAAAAABO0\/s4hnV-Ai7sU\/s1600\/7.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/2.bp.blogspot.com\/-cVWKVNbr2Vc\/URBgka9iCUI\/AAAAAAAABO0\/s4hnV-Ai7sU\/s1600\/7.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EThe above equation can also be represented in an alternating form (AGMA Strength equation) like shown below \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-VdItLzuvk5I\/URBjvwWFw9I\/AAAAAAAABPk\/Gtzaab2kTSw\/s1600\/8.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/3.bp.blogspot.com\/-VdItLzuvk5I\/URBjvwWFw9I\/AAAAAAAABPk\/Gtzaab2kTSw\/s1600\/8.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EWhere J is  \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-By9FXZrUPJg\/URBjwppLj5I\/AAAAAAAABPw\/KQo6EYAA8oo\/s1600\/9.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/4.bp.blogspot.com\/-By9FXZrUPJg\/URBjwppLj5I\/AAAAAAAABPw\/KQo6EYAA8oo\/s1600\/9.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EUsing above equation we can solve for value of b, so we have obtained all the output parameters required for gear design. But such a gear does not guarantee a peacefull operation unless it does not a have enough surface resistance.\u003C\/p\u003E\u003Ch2\u003EDesign for surface resistance\u003C\/h2\u003E\u003Cp\u003EUsually failure happens in gears due to lack of surface resistance, this is also known as pitting failure. Here when 2 mating surfaces come in contact under a specified load a contact stress is developed at contact area and surfaces get deformed. A simple case of contact stress development is depicted below, where 2 cylinders come in contact under a load F.\u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-kYCSHk2X0E4\/URByBWqBKpI\/AAAAAAAABRQ\/FE8IdZdhRyg\/s1600\/surface_contact_stress.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/1.bp.blogspot.com\/-kYCSHk2X0E4\/URByBWqBKpI\/AAAAAAAABRQ\/FE8IdZdhRyg\/s1600\/surface_contact_stress.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.7 Surface deformation and development of surface stress due to load applied\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EFor a gear tooth problem one can determine contact stress as function of following parameters \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-bsa_U9H0vRk\/URBr1kijy2I\/AAAAAAAABQg\/NVx_pFUXQtM\/s1600\/12.gif\" imageanchor=\"1\" style=\"margin-left:1em; margin-right:1em\"\u003E\u003Cimg border=\"0\"  src=\"https:\/\/4.bp.blogspot.com\/-bsa_U9H0vRk\/URBr1kijy2I\/AAAAAAAABQg\/NVx_pFUXQtM\/s1600\/12.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EIf contact stress developed in a gear interface is more than a critical value(specified by AGMA standard), then pitting failure occurs. So designer has to make sure that this condition does not arise.\u003C\/p\u003E   \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/8784643573168582911"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/8784643573168582911"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2013\/02\/spur-gear-design.html","title":"Spur Gear Design"}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"https:\/\/img.youtube.com\/vi\/8bml2pK6Ra0\/default.jpg","height":"72","width":"72"}},{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-7684466259718087804"},"published":{"$t":"2013-01-01T22:05:00.000-08:00"},"updated":{"$t":"2016-04-28T01:14:29.017-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Structural"}],"title":{"type":"text","$t":"Principal stress, Principal plane \u0026 Mohr's circle analysis"},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cdiv dir=\"ltr\" style=\"text-align: left;\" trbidi=\"on\"\u003EConcepts of principal stress and plane form backbone of material stress analysis. Purpose of this video lecture is to give you a good introduction to concept of Principal stress, Principal plane and Mohr’s circle analysis.\u003Cbr \/\u003E\u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe allowfullscreen=\"allowfullscreen\" frameborder=\"0\" height=\"360\" src=\"http:\/\/www.youtube.com\/embed\/Yf59PPHM-eA\" width=\"640\"\u003E\u003C\/iframe\u003E \u003C\/div\u003ESummary of the video lecture is given below \u003Chr\u003E\u003Cbr\u003E\u003Ch2\u003ESummary of Lecture\u003C\/h2\u003E\u003Cul\u003E\u003Cli\u003EEngineers most often wants to determine maximum normal stress induced at a given point for their design purpose. But there can be infinite number of planes passing through a point, and normal stress on each plane will be different from one another.\u003C\/li\u003E\u003Cli\u003EThere will be one plane on which normal stress value is maximum, this plane is known as Principal plane ( more precisely maximum principal plane) and normal stress on this plane is known as principal stress (more precisely maximum principal stress).\u003C\/li\u003E\u003Cli\u003ESimilarly there will be one more plane on which normal stress value is minimum, this is also a principal plane (minimum principal plane) and normal stress on this plane is known as Principal stress (minimum principal stress).\u003C\/li\u003E\u003Cli\u003E2 Dimensional Stress Analysis – Stress acting on a 2D element is shown in figure below\u003C\/li\u003E\u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-YgRZly1H9-s\/UOAn0IJmI4I\/AAAAAAAAAKI\/tfIzh7Sv6Fw\/s1600\/2Dstress.gif\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-YgRZly1H9-s\/UOAn0IJmI4I\/AAAAAAAAAKI\/tfIzh7Sv6Fw\/s1600\/2Dstress.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.1 Stress boundary conditions on a 2 dimensional element\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003Cli\u003EMohr’s circle method is the most easy and convenient way to do stress analysis\u003C\/li\u003E\u003Cli\u003EThe procedure to draw Mohr’s circle for above case is explained below\u003C\/li\u003EStep1 – Draw normal and shear axes with positive axes as shown \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-OVZE42vXWvM\/UOAsiniHREI\/AAAAAAAAAKc\/ywkAa3AbIl0\/s1600\/axes.gif\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-OVZE42vXWvM\/UOAsiniHREI\/AAAAAAAAAKc\/ywkAa3AbIl0\/s1600\/axes.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.2 Normal and shear axes of a Mohr circle\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EStep2 – Mark normal stress values with sign convention, tensile stress is positive and compression stress is negative \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-By9hF5oafNM\/UOAsnd_5uWI\/AAAAAAAAAK8\/E1lna8JqZcM\/s1600\/normal_stress.gif\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-By9hF5oafNM\/UOAsnd_5uWI\/AAAAAAAAAK8\/E1lna8JqZcM\/s1600\/normal_stress.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.3 Marking normal stress values on normal axis\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EStep3 - Draw shear stress values starting from already marked normal stress points. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-26-WqS9-oyU\/UOAsofpCMbI\/AAAAAAAAALE\/n0SKP6kY73c\/s1600\/shear_stress.gif\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-26-WqS9-oyU\/UOAsofpCMbI\/AAAAAAAAALE\/n0SKP6kY73c\/s1600\/shear_stress.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.4 Drawing shear stress values\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EStep4 - Connect end of shear stress lines \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/2.bp.blogspot.com\/-Wp9i3BmqrLg\/UOAsj7frC1I\/AAAAAAAAAKk\/mFR0Phgze2I\/s1600\/diagon.gif\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/2.bp.blogspot.com\/-Wp9i3BmqrLg\/UOAsj7frC1I\/AAAAAAAAAKk\/mFR0Phgze2I\/s1600\/diagon.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.4 Connecting end of shear stress lines\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EStep5 - Draw Mohr’s circle assuming the connection line as diameter of the circle \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E  \u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-TIy8YHf4hKo\/UOAslGlBUfI\/AAAAAAAAAKs\/NoeP0PMs6nE\/s1600\/mohr_circ.gif\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-TIy8YHf4hKo\/UOAslGlBUfI\/AAAAAAAAAKs\/NoeP0PMs6nE\/s1600\/mohr_circ.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.5 Mohr circle construction\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EStep6 – Stress Analysis on Mohr circle - To get normal and shear stress values at any plane theta, take angle 2theta in Mohr circle starting from diagonal of the circle and locate a peripheral point as as shown. Shear stress value will be Y axis value and normal stress value will be X axis value. \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-1m8FjMVUT-w\/UOAsmbqLAJI\/AAAAAAAAAKw\/j18tzUU13SM\/s1600\/mohr_circ_anal.gif\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-1m8FjMVUT-w\/UOAsmbqLAJI\/AAAAAAAAAKw\/j18tzUU13SM\/s1600\/mohr_circ_anal.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.6 Determination on normal and shear stress using Mohr cirlce\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003Cli\u003E3 Dimensional Stress Analysis – Stress boundary condition of a 3 dimensional case is shown in left side of \u0026nbsp;Fig.7. There will be 3 normal stress values induced in a 3 dimensional case, this is shown in right size of the figure.\u003C\/li\u003E\u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-mfyeTBv23IA\/UOA0sLKNCqI\/AAAAAAAAALY\/2OoBH_utVMs\/s1600\/3d-stress-analysis.gif\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/4.bp.blogspot.com\/-mfyeTBv23IA\/UOA0sLKNCqI\/AAAAAAAAALY\/2OoBH_utVMs\/s1600\/3d-stress-analysis.gif\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.7 Stress boundary conditions in a 3 dimensional \u0026nbsp;body and normal stress values induced in it\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E\u003Cli\u003EThere is no graphical method for 3 Dimensional stress analysis, instead we have to use analytical method for this. Values of Principal stress in a 3 dimensional systems are given by solution of following equation.\u003C\/li\u003E\u003C\/ul\u003E\u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-OY1maUbg0Zo\/UOA24mffGmI\/AAAAAAAAALs\/6S4HSy_vWIs\/s1600\/3d-principal-stress-equation.gif\" imageanchor=\"1\" style=\"margin-left: 1em; margin-right: 1em;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-OY1maUbg0Zo\/UOA24mffGmI\/AAAAAAAAALs\/6S4HSy_vWIs\/s1600\/3d-principal-stress-equation.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EWhere values of stress invariants I1,I2 and I3 are given by \u003Cbr \/\u003E\u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-8FUvzinaXNU\/UOA25gD7nEI\/AAAAAAAAALw\/m1HlGIqKreU\/s1600\/stress_invariants.gif\" imageanchor=\"1\" style=\"margin-left: 1em; margin-right: 1em;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-8FUvzinaXNU\/UOA25gD7nEI\/AAAAAAAAALw\/m1HlGIqKreU\/s1600\/stress_invariants.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003E\u003Cbr\u003E\u003Ch2\u003EApplication of Principal Stresses\u003C\/h2\u003E\u003Cp\u003EValues of principal stresses at a given point is vital design information. \u003Ca href=\"https:\/\/www.learnengineering.org\/2012\/12\/theories-of-failure.html\" target=\"_blank\"\u003EMaterial failure theories\u003C\/a\u003E extensively use  this data to predict whether the design will withstand given load at a specified location.\u003C\/div\u003E\u003C\/p\u003E \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/7684466259718087804"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/7684466259718087804"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2013\/01\/principal-stress-plane-mohr-circle.html","title":"Principal stress, Principal plane \u0026 Mohr's circle analysis"}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"https:\/\/img.youtube.com\/vi\/Yf59PPHM-eA\/default.jpg","height":"72","width":"72"}},{"id":{"$t":"tag:blogger.com,1999:blog-7182417135626013721.post-1431353329111524988"},"published":{"$t":"2012-12-29T04:02:00.000-08:00"},"updated":{"$t":"2016-04-27T03:39:28.142-07:00"},"category":[{"scheme":"http://www.blogger.com/atom/ns#","term":"Machine Design"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Mechanics"},{"scheme":"http://www.blogger.com/atom/ns#","term":"Structural"}],"title":{"type":"text","$t":"What is Von Mises Stress ?"},"content":{"type":"html","$t":"\u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003Cscript\u003E  (adsbygoogle = window.adsbygoogle || []).push({     google_ad_client: \"ca-pub-2737347269754935\",     enable_page_level_ads: true   }); \u003C\/script\u003E\u003Cp\u003EVon Mises stress is widely used by designers to check whether their design will withstand a given load condition. In this lecture we will understand Von Mises stress in a logical way.\u003C\/p\u003E\u003Cdiv style=\"text-align: center;\"\u003E\u003Ciframe allowfullscreen=\"allowfullscreen\" frameborder=\"0\" height=\"360\" src=\"http:\/\/www.youtube.com\/embed\/Smj_F7MN3S4\" width=\"640\"\u003E\u003C\/iframe\u003E \u003C\/div\u003EA detailed webpage version of the video lecture along with the industrial applications of Von Mises stress are listed below.\u003Chr\u003E\u003Cbr\u003E  \u003Ch2\u003EUse of Von Mises stress\u003C\/h2\u003E\u003Cp\u003EVon Mises stress is considered to be a safe haven for design engineers.Using this information an engineer can say his design will fail, if the maximum value of Von Mises stress induced in the material is more than strength of the material. It works well for most cases, especially when the material is ductile in nature. In the folowing sections we will have a logical understanding of Von Mises stress and why it is used. \u003C\/p\u003E\u003Ch2\u003EWhen does a material fail?\u003C\/h2\u003E\u003Cp\u003EOne of the most easy way to check when a material fails is a \u003Ci\u003Esimple tension test\u003C\/i\u003E. Here the material is pulled from both ends. When the material reaches the yield point (for ductile material) the material can be considered as failed. The simple tension test is a unidirectional test, this is shown in the first part of Fig.1.  \u003Cdiv align=\"center\" \u003E\u003Ctbody\u003E\u003Cimg alt=\"power flow in automobile\" src=\"https:\/\/1.bp.blogspot.com\/-7oQLDXT9Yw8\/U_gWa6HfE_I\/AAAAAAAADHc\/V5THY0XlynE\/s1600\/Simple_tension_Actual_case.jpg\" \/\u003E\u003Cp\u003E\u003Ctr\u003E\u003Ctd  style=\"text-align: center;\"\u003E\u003Cfont size=\"1.95\"\u003EFig.1 A simple tension test and a real life loading condition \u003C\/font\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/p\u003E\u003C\/div\u003E Now consider the situation in second part of Fig.1, an actual engineering problem with a complex loading condition.  Can we say here also, that the material fails when the maximum normal stress value induced in the material is more than the yield point value ?. If you use such an assumption, you would be using a failure theory called 'normal stress theory'. Many years of engineering experience has shown that normal stress theory doesn’t work in most of the cases. The most preferred failure theory used in industry is ‘Von Mises stress’ based. We will explore what Von Mises stress is in the coming section.\u003C\/p\u003E \u003Ch2\u003EDistortion energy theory\u003C\/h2\u003E\u003Cp\u003EThe concept of Von mises stress arises from the \u003Ci\u003Edistortion energy failure theory\u003C\/i\u003E. Distortion energy failure theory is comparison between 2 kinds of energies, 1) Distortion energy in the actual case 2) Distortion energy in a simple tension case at the time of failure.  According to this theory, failure occurs when the distortion energy in actual case is more than the distortion energy in a \u003Ci\u003Esimple tension case\u003C\/i\u003E at the time of failure. \u003C\/p\u003E \u003Ch2\u003EDistortion energy\u003C\/h2\u003E\u003Cp\u003EIt is the energy required for shape deformation of a material. During pure distortion, the shape of the material changes, but volume does not change. This is illustrated in Fig.2.\u003C\/li\u003E\u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-hbzRDJVGZdY\/UN-gdxGFecI\/AAAAAAAAAJA\/cABMlbYY_2s\/s1600\/distortion.gif\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" height=\"104\" src=\"https:\/\/4.bp.blogspot.com\/-hbzRDJVGZdY\/UN-gdxGFecI\/AAAAAAAAAJA\/cABMlbYY_2s\/s320\/distortion.gif\" width=\"320\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.2 Representation of a pure distortion case\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003EDistortion energy required per unit volume, \u003Cspan style=\"font-size: large;\"\u003Eu\u003C\/span\u003E\u003Cspan style=\"font-size: x-small;\"\u003Ed\u003C\/span\u003E for a general 3 dimensional case is given in terms of \u003Ca href=\"https:\/\/www.learnengineering.org\/2013\/01\/principal-stress-plane-mohr-circle.html\"\u003Eprincipal stress values\u003C\/a\u003E as: \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-wh0nu82eI-4\/UN-jIGTLfgI\/AAAAAAAAAJc\/COjloPyBynw\/s1600\/dist_eqn.gif\" imageanchor=\"1\" style=\"margin-left: 1em; margin-right: 1em;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/4.bp.blogspot.com\/-wh0nu82eI-4\/UN-jIGTLfgI\/AAAAAAAAAJc\/COjloPyBynw\/s1600\/dist_eqn.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003EDistortion energy for \u003Ci\u003Esimple tension case\u003C\/i\u003E at the time of failure is given as: \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-Wskjuq4aLg4\/UN-jJscJ5eI\/AAAAAAAAAJk\/QqExCKERQsk\/s1600\/dist_simp.gif\" imageanchor=\"1\" style=\"margin-left: 1em; margin-right: 1em;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-Wskjuq4aLg4\/UN-jJscJ5eI\/AAAAAAAAAJk\/QqExCKERQsk\/s1600\/dist_simp.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/p\u003E\u003Ch2\u003EExpression for Von Mises stress\u003C\/h2\u003E\u003Cp\u003EThe above 2 quantities can be connected using \u003Ci\u003Edistortion energy failure theory\u003C\/i\u003E, so the condition of failure will be as follows. \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/3.bp.blogspot.com\/-GSYvhjsJzps\/UN-jHFCAACI\/AAAAAAAAAJU\/fK-PN1-2W3I\/s1600\/dist_cond.gif\" imageanchor=\"1\" style=\"margin-left: 1em; margin-right: 1em;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/3.bp.blogspot.com\/-GSYvhjsJzps\/UN-jHFCAACI\/AAAAAAAAAJU\/fK-PN1-2W3I\/s1600\/dist_cond.gif\" \/\u003E\u003C\/a\u003E\u003Cspan style=\"text-align: left;\"\u003E\u0026nbsp;\u003C\/span\u003E\u003C\/div\u003EThe left hand side of the above equation is denoted as Von Mises stress. \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/1.bp.blogspot.com\/-0PEFWEx8bTQ\/UN-jMRhN9iI\/AAAAAAAAAJw\/U88fGQeA8FE\/s1600\/von_stress.gif\" imageanchor=\"1\" style=\"margin-left: 1em; margin-right: 1em;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/1.bp.blogspot.com\/-0PEFWEx8bTQ\/UN-jMRhN9iI\/AAAAAAAAAJw\/U88fGQeA8FE\/s1600\/von_stress.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003ESo as a failure criterion, the engineer can check whether Von Mises stress induced in the material exceeds yield strength (for ductile material) of the material.So the failure condition can be simplified as \u003Cdiv class=\"separator\" style=\"clear: both; text-align: center;\"\u003E\u003Ca href=\"https:\/\/4.bp.blogspot.com\/-79ag29IlhZ4\/UN-jK5dhjwI\/AAAAAAAAAJs\/MGDGzSwwtKQ\/s1600\/fina_condn.gif\" imageanchor=\"1\" style=\"margin-left: 1em; margin-right: 1em;\"\u003E\u003Cimg border=\"0\" src=\"https:\/\/4.bp.blogspot.com\/-79ag29IlhZ4\/UN-jK5dhjwI\/AAAAAAAAAJs\/MGDGzSwwtKQ\/s1600\/fina_condn.gif\" \/\u003E\u003C\/a\u003E\u003C\/div\u003E\u003C\/p\u003E \u003Ch2\u003EIndustrial Application of Von Mises Stress\u003C\/h2\u003E\u003Cp\u003EDistortion energy theory is the most preferred failure theory used in industry. It is clear from above discussions that whenever an engineer resorts to distortion energy theory he can use Von Mises stress as a failure criterion.Let's see one example:\u003C\/p\u003E\u003Cp\u003ESuppose an engineer has to design a cantilever beam using mild steel as the material, with a load capacity of 10000 N. The materials properties of mild steel are also shown in the figure. The yield stress value of mild steel is 2.5x10\u003Csup\u003E8\u003C\/sup\u003E Pa. He wants to check whether his design will withstand the design load.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh6.googleusercontent.com\/-Rzzldtg8gMI\/UhTRwHDBFjI\/AAAAAAAACig\/eTq7CYLhvy4\/s1600\/von-mises-problem.jpg\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" height=\"190\" src=\"https:\/\/lh6.googleusercontent.com\/-Rzzldtg8gMI\/UhTRwHDBFjI\/AAAAAAAACig\/eTq7CYLhvy4\/s1600\/von-mises-problem.jpg\" width=\"587\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.3 A design problem, the cantilever should be able to withstand design load\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E  The following figure shows the Von Mises stress distribution obtained by FEA analysis of the beam.  \u003Ctable align=\"center\" cellpadding=\"0\" cellspacing=\"0\" class=\"tr-caption-container\" style=\"margin-left: auto; margin-right: auto; text-align: center;\"\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd style=\"text-align: center;\"\u003E\u003Ca href=\"https:\/\/lh4.googleusercontent.com\/-PZhF5ojSXoM\/UhTRz-BonRI\/AAAAAAAACio\/Q-9f4kTswUU\/s1600\/von_mises_stress.jpg\" imageanchor=\"1\" style=\"margin-left: auto; margin-right: auto;\"\u003E\u003Cimg border=\"0\" height=\"190\" src=\"https:\/\/lh4.googleusercontent.com\/-PZhF5ojSXoM\/UhTRz-BonRI\/AAAAAAAACio\/Q-9f4kTswUU\/s1600\/von_mises_stress.jpg\" width=\"582\" \/\u003E\u003C\/a\u003E\u003C\/td\u003E\u003C\/tr\u003E\u003Ctr\u003E\u003Ctd class=\"tr-caption\" style=\"text-align: center;\"\u003EFig.4 Distribution of Von Mises stress in the beam obtained from FEA analysis\u003C\/td\u003E\u003C\/tr\u003E\u003C\/tbody\u003E\u003C\/table\u003E One can note that Von Mises stress is at maximum towards the fixed end of the beam, and the value is 1.32x10\u003Csup\u003E8\u003C\/sup\u003E Pa. This is less than the yield point value of mild steel. So the design is safe.  In short an engineer's duty is to keep the maximum value of Von Mises stress induced in the material less than its strength.\u003C\/p\u003E \u003Cscript async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"\u003E\u003C\/script\u003E\u003C!-- Responsive ad --\u003E\u003Cins class=\"adsbygoogle\"      style=\"display:block\"      data-ad-client=\"ca-pub-2737347269754935\"      data-ad-slot=\"7774217985\"      data-ad-format=\"auto\"\u003E\u003C\/ins\u003E\u003Cscript\u003E(adsbygoogle = window.adsbygoogle || []).push({}); \u003C\/script\u003E"},"link":[{"rel":"edit","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/1431353329111524988"},{"rel":"self","type":"application/atom+xml","href":"http:\/\/www.blogger.com\/feeds\/7182417135626013721\/posts\/default\/1431353329111524988"},{"rel":"alternate","type":"text/html","href":"http:\/\/www.learnengineering.org\/2012\/12\/what-is-von-mises-stress.html","title":"What is Von Mises Stress ?"}],"author":[{"name":{"$t":"Sabin M"},"uri":{"$t":"https:\/\/plus.google.com\/113983923192891667856"},"email":{"$t":"noreply@blogger.com"},"gd$image":{"rel":"http://schemas.google.com/g/2005#thumbnail","width":"32","height":"32","src":"\/\/lh4.googleusercontent.com\/-7s2C1CoKPjM\/AAAAAAAAAAI\/AAAAAAAADuk\/p4kg_Q3BKZA\/s512-c\/photo.jpg"}}],"media$thumbnail":{"xmlns$media":"http://search.yahoo.com/mrss/","url":"https:\/\/img.youtube.com\/vi\/Smj_F7MN3S4\/default.jpg","height":"72","width":"72"}}]}});