\n\t\t\t\t\t\t\tTable 1. Example of some selected angular input/output displacements, unit: degree
\n\n
\n\nThe research leading to these results has received funding from the European Community\'s Seventh Framework Programme (FP7/2007-2013) under grant agreement number 285417. The publishing of this book was funded by the EC FP7 Post-Grant Open Access Pilot programme. ',isbn:"978-953-51-3376-6",printIsbn:"978-953-51-3375-9",pdfIsbn:"978-953-51-4699-5",doi:"10.5772/intechopen.68449",price:119,priceEur:129,priceUsd:155,slug:"search-and-rescue-robotics-from-theory-to-practice",numberOfPages:262,isOpenForSubmission:!1,isInWos:1,hash:"e1ca88810595580ec90815aab3f1ec9a",bookSignature:"",publishedDate:"August 23rd 2017",coverURL:"https://cdn.intechopen.com/books/images_new/6181.jpg",numberOfDownloads:222995,numberOfWosCitations:10,numberOfCrossrefCitations:30,numberOfDimensionsCitations:41,hasAltmetrics:1,numberOfTotalCitations:81,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"March 10th 2017",dateEndSecondStepPublish:"March 31st 2017",dateEndThirdStepPublish:"June 27th 2017",dateEndFourthStepPublish:"September 25th 2017",dateEndFifthStepPublish:"November 24th 2017",currentStepOfPublishingProcess:1,indexedIn:"1,2,3,4,5,6,7",editedByType:"Authored by",kuFlag:!1,editors:null,equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"1250",title:"Rescue Robot",slug:"rescue-robot"}],chapters:[{id:"56152",title:"Introduction to the Use of Robotic Tools for Search and Rescue",doi:"10.5772/intechopen.69489",slug:"introduction-to-the-use-of-robotic-tools-for-search-and-rescue",totalDownloads:23334,totalCrossrefCites:9,totalDimensionsCites:13,signatures:"Geert De Cubber, Daniela Doroftei, Konrad Rudin, Karsten Berns,\nAnibal Matos, Daniel Serrano, Jose Sanchez, Shashank Govindaraj,\nJanusz Bedkowski, Rui Roda, Eduardo Silva and Stephane Ourevitch",downloadPdfUrl:"/chapter/pdf-download/56152",previewPdfUrl:"/chapter/pdf-preview/56152",authors:[{id:"206420",title:"Dr.",name:"Geert",surname:"De Cubber",slug:"geert-de-cubber",fullName:"Geert De Cubber"}],corrections:null},{id:"56037",title:"User-Centered Design",doi:"10.5772/intechopen.69483",slug:"user-centered-design",totalDownloads:22007,totalCrossrefCites:1,totalDimensionsCites:2,signatures:"Daniela Doroftei, Geert De Cubber, Rene Wagemans, Anibal Matos,\nEduardo Silva, Victor Lobo, Guerreiro Cardoso, Keshav Chintamani,\nShashank Govindaraj, Jeremi Gancet and Daniel Serrano",downloadPdfUrl:"/chapter/pdf-download/56037",previewPdfUrl:"/chapter/pdf-preview/56037",authors:[{id:"82804",title:"Ms.",name:"Daniela",surname:"Doroftei",slug:"daniela-doroftei",fullName:"Daniela Doroftei"},{id:"153104",title:"Prof.",name:"Victor",surname:"Lobo",slug:"victor-lobo",fullName:"Victor Lobo"}],corrections:null},{id:"56050",title:"Unmanned Aerial Systems",doi:"10.5772/intechopen.69490",slug:"unmanned-aerial-systems",totalDownloads:22077,totalCrossrefCites:3,totalDimensionsCites:5,signatures:"Rudin Konrad, Daniel Serrano and Pascal Strupler",downloadPdfUrl:"/chapter/pdf-download/56050",previewPdfUrl:"/chapter/pdf-preview/56050",authors:[{id:"212085",title:"Mr.",name:"Konrad",surname:"Rudin",slug:"konrad-rudin",fullName:"Konrad Rudin"}],corrections:null},{id:"56080",title:"Unmanned Ground Robots for Rescue Tasks",doi:"10.5772/intechopen.69491",slug:"unmanned-ground-robots-for-rescue-tasks",totalDownloads:23230,totalCrossrefCites:3,totalDimensionsCites:3,signatures:"Karsten Berns, Atabak Nezhadfard, Massimo Tosa, Haris Balta and\nGeert De Cubber",downloadPdfUrl:"/chapter/pdf-download/56080",previewPdfUrl:"/chapter/pdf-preview/56080",authors:[{id:"212086",title:"Prof.",name:"Karsten",surname:"Berns",slug:"karsten-berns",fullName:"Karsten Berns"}],corrections:null},{id:"56139",title:"Unmanned Maritime Systems for Search and Rescue",doi:"10.5772/intechopen.69492",slug:"unmanned-maritime-systems-for-search-and-rescue",totalDownloads:22047,totalCrossrefCites:2,totalDimensionsCites:6,signatures:"Aníbal Matos, Eduardo Silva, José Almeida, Alfredo Martins, Hugo\nFerreira, Bruno Ferreira, José Alves, André Dias, Stefano Fioravanti,\nDaniele Bertin and Victor Lobo",downloadPdfUrl:"/chapter/pdf-download/56139",previewPdfUrl:"/chapter/pdf-preview/56139",authors:[{id:"153104",title:"Prof.",name:"Victor",surname:"Lobo",slug:"victor-lobo",fullName:"Victor Lobo"},{id:"12282",title:"Dr.",name:"Aníbal",surname:"Matos",slug:"anibal-matos",fullName:"Aníbal Matos"}],corrections:null},{id:"56126",title:"Interoperability in a Heterogeneous Team of Search and Rescue Robots",doi:"10.5772/intechopen.69493",slug:"interoperability-in-a-heterogeneous-team-of-search-and-rescue-robots",totalDownloads:22075,totalCrossrefCites:6,totalDimensionsCites:6,signatures:"Daniel Serrano López, German Moreno, Jose Cordero, Jose Sanchez,\nShashank Govindaraj, Mario Monteiro Marques, Victor Lobo,\nStefano Fioravanti, Alberto Grati, Konrad Rudin, Massimo Tosa,\nAnibal Matos, Andre Dias, Alfredo Martins, Janusz Bedkowski, Haris\nBalta and Geert De Cubber",downloadPdfUrl:"/chapter/pdf-download/56126",previewPdfUrl:"/chapter/pdf-preview/56126",authors:[{id:"153104",title:"Prof.",name:"Victor",surname:"Lobo",slug:"victor-lobo",fullName:"Victor Lobo"},{id:"212087",title:"Mr.",name:"Daniel",surname:"Serrano",slug:"daniel-serrano",fullName:"Daniel Serrano"}],corrections:null},{id:"56257",title:"Tactical Communications for Cooperative SAR Robot Missions",doi:"10.5772/intechopen.69494",slug:"tactical-communications-for-cooperative-sar-robot-missions",totalDownloads:21867,totalCrossrefCites:0,totalDimensionsCites:0,signatures:"José Manuel Sanchez, José Cordero, Hafeez M. Chaudhary, Bart\nSheers and Yudani Riobó",downloadPdfUrl:"/chapter/pdf-download/56257",previewPdfUrl:"/chapter/pdf-preview/56257",authors:[{id:"212088",title:"Mr.",name:"Jose",surname:"Sanchez",slug:"jose-sanchez",fullName:"Jose Sanchez"}],corrections:null},{id:"56086",title:"Command and Control Systems for Search and Rescue Robots",doi:"10.5772/intechopen.69495",slug:"command-and-control-systems-for-search-and-rescue-robots",totalDownloads:22302,totalCrossrefCites:2,totalDimensionsCites:2,signatures:"Shashank Govindaraj, Pierre Letier, Keshav Chintamani, Jeremi\nGancet, Mario Nunez Jimenez, Miguel Ángel Esbrí, Pawel Musialik,\nJanusz Bedkowski, Irune Badiola, Ricardo Gonçalves, António\nCoelho, Daniel Serrano, Massimo Tosa, Thomas Pfister and Jose\nManuel Sanchez",downloadPdfUrl:"/chapter/pdf-download/56086",previewPdfUrl:"/chapter/pdf-preview/56086",authors:[{id:"212089",title:"Mr.",name:"Shashank",surname:"Govindaraj",slug:"shashank-govindaraj",fullName:"Shashank Govindaraj"}],corrections:null},{id:"56052",title:"ICARUS Training and Support System",doi:"10.5772/intechopen.69496",slug:"icarus-training-and-support-system",totalDownloads:22057,totalCrossrefCites:1,totalDimensionsCites:1,signatures:"Janusz Będkowski, Karol Majek, Michal Pełka, Andrzej Masłowski,\nAntonio Coelho, Ricardo Goncalves, Ricardo Baptista and Jose\nManuel Sanchez",downloadPdfUrl:"/chapter/pdf-download/56052",previewPdfUrl:"/chapter/pdf-preview/56052",authors:[{id:"63695",title:"Dr.",name:"Janusz",surname:"Bȩdkowski",slug:"janusz-bdkowski",fullName:"Janusz Bȩdkowski"}],corrections:null},{id:"56145",title:"Operational Validation of Search and Rescue Robots",doi:"10.5772/intechopen.69497",slug:"operational-validation-of-search-and-rescue-robots",totalDownloads:22012,totalCrossrefCites:3,totalDimensionsCites:3,signatures:"Geert De Cubber, Daniela Doroftei, Haris Balta, Anibal Matos,\nEduardo Silva, Daniel Serrano, Shashank Govindaraj, Rui Roda,\nVictor Lobo, Mário Marques and Rene Wagemans",downloadPdfUrl:"/chapter/pdf-download/56145",previewPdfUrl:"/chapter/pdf-preview/56145",authors:[{id:"206420",title:"Dr.",name:"Geert",surname:"De Cubber",slug:"geert-de-cubber",fullName:"Geert De Cubber"},{id:"153104",title:"Prof.",name:"Victor",surname:"Lobo",slug:"victor-lobo",fullName:"Victor Lobo"}],corrections:null}],productType:{id:"3",title:"Monograph",chapterContentType:"chapter",authoredCaption:"Authored by"}},relatedBooks:[{type:"book",id:"5905",title:"Robots Operating in Hazardous Environments",subtitle:null,isOpenForSubmission:!1,hash:"a22b4e4b02af1dd0727231b0d974f121",slug:"robots-operating-in-hazardous-environments",bookSignature:"Hüseyin Canbolat",coverURL:"https://cdn.intechopen.com/books/images_new/5905.jpg",editedByType:"Edited by",editors:[{id:"5887",title:"Dr.",name:"Hüseyin",surname:"Canbolat",slug:"huseyin-canbolat",fullName:"Hüseyin Canbolat"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],ofsBooks:[]},correction:{item:{id:"67321",slug:"corrigendum-to-clinical-approach-in-the-diagnosis-of-acute-appendicitis",title:"Corrigendum to: Clinical Approach in the Diagnosis of Acute Appendicitis",doi:null,correctionPDFUrl:"https://cdn.intechopen.com/pdfs/67321.pdf",downloadPdfUrl:"/chapter/pdf-download/67321",previewPdfUrl:"/chapter/pdf-preview/67321",totalDownloads:null,totalCrossrefCites:null,bibtexUrl:"/chapter/bibtex/67321",risUrl:"/chapter/ris/67321",chapter:{id:"61365",slug:"clinical-approach-in-the-diagnosis-of-acute-appendicitis",signatures:"Alfredo Alvarado",dateSubmitted:"September 14th 2017",dateReviewed:"February 16th 2018",datePrePublished:null,datePublished:"June 27th 2018",book:{id:"6471",title:"Current Issues in the Diagnostics and Treatment of Acute Appendicitis",subtitle:null,fullTitle:"Current Issues in the Diagnostics and Treatment of Acute Appendicitis",slug:"current-issues-in-the-diagnostics-and-treatment-of-acute-appendicitis",publishedDate:"June 27th 2018",bookSignature:"Dmitry Victorovich Garbuzenko",coverURL:"https://cdn.intechopen.com/books/images_new/6471.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"108808",title:"Prof.",name:"Dmitry",middleName:"Victorovich",surname:"Garbuzenko",slug:"dmitry-garbuzenko",fullName:"Dmitry Garbuzenko"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"221775",title:"M.D.",name:"Alfredo",middleName:null,surname:"Alvarado",fullName:"Alfredo Alvarado",slug:"alfredo-alvarado",email:"alfredoalvara@hotmail.com",position:null,institution:null}]}},chapter:{id:"61365",slug:"clinical-approach-in-the-diagnosis-of-acute-appendicitis",signatures:"Alfredo Alvarado",dateSubmitted:"September 14th 2017",dateReviewed:"February 16th 2018",datePrePublished:null,datePublished:"June 27th 2018",book:{id:"6471",title:"Current Issues in the Diagnostics and Treatment of Acute Appendicitis",subtitle:null,fullTitle:"Current Issues in the Diagnostics and Treatment of Acute Appendicitis",slug:"current-issues-in-the-diagnostics-and-treatment-of-acute-appendicitis",publishedDate:"June 27th 2018",bookSignature:"Dmitry Victorovich Garbuzenko",coverURL:"https://cdn.intechopen.com/books/images_new/6471.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"108808",title:"Prof.",name:"Dmitry",middleName:"Victorovich",surname:"Garbuzenko",slug:"dmitry-garbuzenko",fullName:"Dmitry Garbuzenko"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"221775",title:"M.D.",name:"Alfredo",middleName:null,surname:"Alvarado",fullName:"Alfredo Alvarado",slug:"alfredo-alvarado",email:"alfredoalvara@hotmail.com",position:null,institution:null}]},book:{id:"6471",title:"Current Issues in the Diagnostics and Treatment of Acute Appendicitis",subtitle:null,fullTitle:"Current Issues in the Diagnostics and Treatment of Acute Appendicitis",slug:"current-issues-in-the-diagnostics-and-treatment-of-acute-appendicitis",publishedDate:"June 27th 2018",bookSignature:"Dmitry Victorovich Garbuzenko",coverURL:"https://cdn.intechopen.com/books/images_new/6471.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"108808",title:"Prof.",name:"Dmitry",middleName:"Victorovich",surname:"Garbuzenko",slug:"dmitry-garbuzenko",fullName:"Dmitry Garbuzenko"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}}},ofsBook:{item:{type:"book",id:"8661",leadTitle:null,title:"Statistical Machine Learning",subtitle:null,reviewType:"peer-reviewed",abstract:"
\r\n\tStatistical machine learning merges statistics with machine learning which falls in the field of computer science, systems science and optimization. Much of the agenda in statistical machine learning is driven by applied problems in science and technology, where data streams are increasingly large-scale, dynamical and heterogeneous, and where mathematical and algorithmic creativity are required to bring statistical methodology to bear. Fields such as bioinformatics, artificial intelligence, signal processing, communications, networking, and information are all intervened here.
\r\n\tStatistical machine learning specifically poses some of the most challenging theoretical problems in modern statistics, the crucial among them being the general problem of understanding the link between inference and computation. This book intends to provide the reader with a comprehensive overview of linear method for regression, non linear method for regression, deep learning, unsupervised learning, artificial neural network, and support vector machine (SVM).
Globoidal cam mechanisms are widely used in industry. Compared to other cam-follower systems, the globoidal cam-follower mechanisms have many advantages, such as: compact structure, high loading capacity, low noise, low vibration, and high reliability. They are widely used in machine tools, automatic assembly lines, paper processing machines, packing machines, and many automated manufacturing devices.
\n\t\t\tIn term of the shape, globoidal cam is one of the most complicated cams. The most important task when modelling the globoidal cams is to represent their working surfaces. The working surfaces of the globoidal cams are the surfaces that contact with the roller surfaces. These surfaces are very complex and it is very difficult to create them accurately.
\n\t\t\tUp to now, a number of works dealing with finding the way to describe accurately these surfaces have been proposed.
\n\t\t\tSome researchers derived mathematically expressions for the surface geometry of the globoidal cam with cylindrical, hyperboloid, or spherical rollers, based on coordinate transformation, differential geometry, and theory of conjugate surfaces (Yan & Chen, 1994& 1995; Yan-ming, 2000; Cheng, 2002; Lee & Lee, 2001& 2007; Chen & Hong, 2008). They developed their own programs, which were written in Visual Basic, C or C++ languages, to assist themselves in studying. Some programs can draw and display the draft of the cam contour, or create the solid model. Some can create the data of the cam curve profile which will be the input data for CAD/CAM software such as Unigraphics to build the CAD model (Chen & Hong, 2008). Some other researchers also described mathematicaly the cam surface, but they used computer to develop a package, which was a combination of AutoCAD R14, 3D Studio Max, and VBA, to generate the surfaces of the roller gear cam (En-hui et al., 2001). In addition, some researchers studied to create the globoidal cam with conical rollers from machining point of view (Tsay & Lin, 2006). They represented the surface geometry of the cam as the swept surfaces of the tool paths. In their study, the expression of a surface normal, a rule surface and its offset, meshing vectors and meshing angles were introduced to define the accurate swept surfaces generated by the roller follower, and a program in C++ language developed to generate the surface coordinates of the cam.
\n\t\t\tIn general, the works mentioned above have used the mathematical expressions for the globoidal cam surfaces and various cam laws as the input data to generate the cam surfaces. From machining point of view, the globoidal cam surfaces can be determined by corresponding angular displacements of both the cam and the driven member (Koloc & Vaclavik, 1993). These angular displacements can be extracted from the NC program generated by some special sofwares that are specialized for cam mechanisms. They can also be obtained from the follower displacement equations. In this study, the concave globoidal cam with swinging roller follower is modeled from angular input and output displacements.
\n\t\t\tThe objective of the chapter is to introduce some effective methods for modelling concave globoidal cam. These methods can be implemented by using commercial CAD/CAM sofwares. In the chapter, Pro/ENGINEER® Wildfire 2.0 is used to create the cams for the illustrative example that we have recently done for industry in Czech Republic. In this case study, the input data for modelling are the angular input and output displacements of the cam and the follower. Furthermore, besides modelling methods, some important techniques that are useful for designers to find out the most accurate model are also represented. In this chapter, the terms “globoidal cam surface(s)” and “cam surface(s)” refer the working surface(s) of the globoidal cam.
\n\t\t\tThe outline of the chapter is as follows. Section 2 presents the theoretical background of concave globoidal cam. In section 3 we describe in detail some modelling methods that can be used to create the globoidal cam surfaces. An application example is presented in Section 4. Finally, conclusion remarks are given in Section 5.
\n\t\tThere are two types of globoidal cams. The first one is the globoidal cam that has a groove on its surface and the roller follower oscillates when the cam rotates. This type has two subtypes which are convex and concave (Figure 1). These cams are used for small angles of follower oscillation. The second one has one or more ribs on a globoidal body. This type is also called roller gear cam or Ferguson drive (Rothbart, 2004). The two surfaces of the rib always contact with the rollers (cylindrical, spherical or conical) of the follower. This follower may oscillate about its axis or have an intermittent rotation. Figure 2 shows two subtypes of the concave globoidal cam: the concave globoidal cam with an oscillating follower and the concave globoidal cam with an indexing turret follower. The rib of these cams looks like a thread or a blade so that sometimes they can be called thread-type or blade-type globoidal cams. In this study, the single thread-type is the globoidal cam that we will deal with.
\n\t\t\t\n\t\t\t\tFigure 3 illustrates the geometrical relationships between a concave globoidal cam with an oscillating follower. According to the structure of the globoidal cam, as can be seen from Figure 2&3, the symmetrical plane of the follower contains the cam axis and the axes of the rollers intersect at a point that lies on the follower axis. In Figure 3, the development plane is the plane that is normal to the axis of the roller and located anywhere along the length of the roller. The intersection point between the development plane and the axis of the roller is the pitch point (P). Datum plane is the plane normal to the cam axis and contains the follower axis. The angular displacement of the roller is measured from this plane.
\n\t\t\tThe following are some parameters related to a globoidal cam-follower system (Koloc & Vaclavik, 1993; Reeve, 1995).
\n\t\t\tGloboidal cam-groove type, oscillating follower
Globoidal cam - thread type.
- angular input displacement (the rotation angle of the cam).
- angular output displacement from datum plane (the rotation angle of the follower). has a relationship with and it can be expressed by function = f(), (En-hui et al., 2001).
\n\t\t\t\t\t\t0 – angle from datum plane to start of follower motion, measured in direction of motion. If the start point is encountered after the datum plane then 0 is positive.
\n\t\t\t\t\t\t1 – angle between the axis of the upper roller with the datum plane. At the beginning, when the upper roller is at the starting point then 0= 1.
\n\t\t\t\t\t\t2 – angle between the axis of the lower roller with the datum plane.
t - distance between the axis of the follower to the end of the roller, measured along the roller axis.
e – clearance between the end of the roller and the cam body.
F - distance from the axis of the follower to the pitch point.
C - distance between the cam axis and the turret axis.
R - perpendicular distance from cam axis to the pitch point, expressed as
\n\t\t\t\t\t\t\n\t\t\t\t\t\t
h – distance from the pitch point to the datum plane. It is the height of the point P and presented as
\n\t\t\t\t\t\t\n\t\t\t\t\t\t
Obviously, the coordinates of the pitch points on the rollers can be calculated if the angular input and output displacements are known. From these coordinates and some other information, the pitch surfaces of the cam can be modeled.
\n\t\t\tGloboidal cam- oscillating follower arrangement
There are some methods used to model concave globoidal cams. The most important task in the modelling procedure is to create the working surfaces of the cam. Once these surfaces are created, other surfaces of the cam can be easily formed later. Here, we introduce two groups of methods that can be used to create the cam surfaces, namely Pitch surface-based methods and Standard cutter-based method.
\n\t\t\tIn a globoidal cam-follower system, when the follower rotates, the locus of the roller axis will generate a ruled surface (pitch curved surface) in space (Tsay & Lin, 2006). The two axes of two rollers in this case study will generate two pitch curved surfaces. The working surfaces of the cam can be obtained from the pitch surfaces by offsetting them a distance that is equal to the radius of the roller.
\n\t\t\t\tThere are several methods to get the pitch surface. The followings are three methods that can be used to create the pitch surface.
\n\t\t\t\tSweep a straight line with two constraints (Figure 4): (i) the angle between this line and the datum plane varies when the cam rotates and its value is i\n\t\t\t\t\t\tj; (ii) the coordinates of the pitch point P on this line, in the cylindrical coordinate system, corresponding with the input angular displacement j, satisfy the formulas below.
\n\t\t\t\t\twhere i = 1, 2, corresponding with the upper and the lower pitch surfaces; j = 1,2,…,n, corresponding with the angular output displacements.
\n\t\t\t\t\tThe relationship between pairs and , h and , R and can be expressed in graphs. These graphs are useful for modelling the cam in commercial CAD/CAM softwares.
\n\t\t\t\tPrinciple of graphs-based method
This method is similar to the previous method but here the two pitch surfaces are created at the same time. These surfaces are made by sweeping an “open section” which consists of three straight lines. Two of them are collinear with the axes of the two rollers. The last one connects them together.
\n\t\t\t\tSweep a straight line that is collinear with the roller axis. The two end points of this line must lie on two curves (Figure 6). One of these curves is a circle in the datum plane. This circle goes through the intersection point of the roller axes and its center is in the cam axis and it is also called the origin trajectory. The other curve is a three-dimensional (3D) curve. This 3D curve is the locus of a point, which located on the roller axis (it can be the pitch point), when the follower rotating. The coordinates of that point satisfy formulas (3) and (4) above.
\n\t\t\t\t\t“Open section” method
Principle of curves- based method
An end mill cutter can generate the surfaces of a globoidal cam. If the diameters of the cutter and the roller are equal, the motion of the cutter will be similar to that of the roller in the machining process, and of course, the cutter must rotate about its axis (roller axis). The sweep surface of the tool path can represent the working surface of the cam. The following is one way that can be used to get the cam surface.
\n\t\t\t\t\tCut a bank by sweeping a rectangular section (Figure 7) to form the cam surfaces if the following constrains are performed:
\n\t\t\t\t\tThe width of the section is equal to the diameter of the roller. The length of the section satisfies the following formula.
\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
where, L is the length of the rectangular section, t and e are two geometrical parameters of the cam which mentioned in section 2.
Two points on the section, which are intersection points between the symmetry axis of the section and its edges, must follow two 3D curves. These curves are loci of two points, which are on the roller axis, when the follower rotates. One of these curves is the origin trajectory. The curves which are used in the curves- based method can be applied here.
This section plane always contains the cam axis.
Standard cutter-based method
The globoidal cam can be modeled by using CAD/CAM softwares such as CATIA, Unigraphics NX, Pro/Engineer.... The four methods above can be implemented in Pro/Engineer. In theory, geometric errors may exist on every model. These errors may be so very high that the model cannot be acceptable. Hence, after modelling, models must be checked to find out the best one among them. In this study, Pro/Engineer Wildfire 2.0 is used to create the globoidal cam. The implementation of those methods is presented in a form of an illustrated example in the next section. Besides, some other important tasks to check the model are included as well.
\n\t\t\t\tGiven a concave globoidal cam with an oscillating follower that has two cylindrical rollers. The angle between two axes of the rollers is 600. The increment of the input angle of the cam is 0.20, starts from 0 and ends at 3600. The angular input and output displacements are given in a table that consists of 1800 pairs of corresponding angles. Some of them are presented in Table I in the appendix. To observe easily, the relationship between the angular input and output displacements is showed in Figure 8. The following are some other parameters of the system, which are showed in Figure 2: d = 25.5 mm, l = 16 mm, C= 107.8 mm, t = 58.7 mm, 0 = 7.490, e = 2.3 mm.
\n\t\t\t\tThere are some calculations that must be done before making the models as follows:
\n\t\t\t\tCalculating the angular outputs included 0.
Calculating the angle
\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t
and
\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t
Angular input/output displacements
The following are the main steps to create the globoidal cam by using four methods described above in Pro/Engineer Wildfire 2.0. The accuracy of the system is set to 0.0005 to get high accurate models.
\n\t\t\t\t\n\t\t\t\t\tThe graphs-based method\n\t\t\t\t
\n\t\t\t\tCreate a revolution surface of the globoidal body of the cam (Figure 9a).
Create 3 graphs for the angle between the sweeping line and the datum plane (Figure 9b), the height of the pitch point on the sweeping line, and the distance (radius) from the pitch point to the cam axis. These graphs show the dependence of the three above parameters on the angular output displacement of the cam.
Create the upper pitch surface by using the Variable Section Sweep command (Figure 9c). The origin trajectory in this case is the circle which is the intersection between datum plane and the cam body. Constrains for this command are formulas that have the form as
\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t
where
- sd# is the dimension which will vary. It can be R or h or (Figure 3a).
- graph_name is the name of the graph which created in step 2, corresponding with the dimension sd#.
Refer (Tuong & Pokorny, 2008b) to get some more useful infomation about these graphs.
(4) Repeat steps 2 and 3 for the lower pitch surface (Figure 9c), using other three graphs.
(5) Offset the two pitch surfaces to get the working surfaces of the cam (Figure 9d).
(6) Merge all surfaces to become one and convert the united surface to solid (Figure 9e).
(7) Perform some extra cuts to get the desired cam, model 1 (Figure 9f).
Main steps of the graphs-based method
\n\t\t\t\t\tThe open section-based method\n\t\t\t\t
\n\t\t\t\tCreate a revolution surface and 3 graphs like the first two steps in the first method.
(Create the two pitch surfaces at the same time by using the Variable Section Sweep command (Figure 10a) with the same constrains in step 3 in the first method.
Perform steps 5, 6 & 7 as in the first method to get the solid model (Figure 10b) and the desired cam, model 2 (Figure 10c).
Some main steps of the open section-based method
\n\t\t\t\t\tThe curves-based method\n\t\t\t\t
\n\t\t\t\tCreate a revolution surface of the globoidal body of the cam (Figure 11a).
Create the origin trajectory and two 3D curves (Figure 11b).
Create the two pitch surfaces by using the Variable Section Sweep command (Figure 11c).
Perform steps 5, 6 & 7 as in the first method to get the offset surfaces (Figure 11d), the solid model (Figure 11e) and the desired cam, model 3 (Figure 11f).
Main steps of the curves-based method
\n\t\t\t\t\tThe standard cutter-based method\n\t\t\t\t
\n\t\t\t\tCreate a revolution blank of the cam body (Figure 12a).
Create the origin trajectory and two 3D curves (Figure 12b).
Perform two cuts with rectangular section by using the Variable Section Sweep command (Figure 12c).
Perform some extra cuts to get the desired cam, model 4 (Figure 12d).
Main steps of the standard cutter-based method
Among the four methods, the two first methods need more steps than the others but the modelling time is much shorter than that of the two last methods. This is because when creating the pitch surfaces in the methods which need 3D curves, the system has to interpolate the swept surface through 1800 physical points on this curve.
\n\t\t\t\tTo see the cam easily, the pitch surfaces on four final models in figures 9 to 12 are hidden. In general, these models look great and similar. In order to choose the best one among them, the interference between the cam and its rollers must be checked. If there is no interference and the clearance between the components is small enough, then the result is acceptable.
\n\t\t\tIn order to make animation and verify the interference between components in the globoidal cam mechanism, first, an assembly of the cam and the follower is made. After that, use the Mechanism Design module to define the geometrical relationships of the system, make it move and analyze its motion also. Last, use a kinematics analysis to obtain information on interference between components. The following is the procedure to make animation and check interference.
\n\t\t\t\tCreating the assembly model.
Modifying Joint Axis Settings.
Creating a slot-follower.
Checking the assembly model.
Creating servo motor.
Creating and Running Analyses.
Viewing results and taking measurements.
When the globoidal cam rotates, the follower will stay or rotate depending on the location of the rollers on the cam surfaces. The follower will not move when the rollers still contact with the cam surfaces in the dwell periods. To get a motion for the follower, a point on one roller axis has to trace along a 3D curve on the pitch surface. The pitch point now can be used for this purpose (point PNT0 in Figure 13). This 3D curve is available on the model 3 and model 4. This curve can be drawn on model 1 and model 2 for the purpose of checking interference. The servo motor is always applied on the cam axis so that the cam can move about its axis. Servo motor can also be applied for the follower. In this case, the slot-follower connection is omitted. Figure 13 shows the cam-follower system in the Mechanism application with the slot-follower connection.
\n\t\t\t\tCam-follower system in Mechanism application.
During the animation, the motions of the cam and the follower are simulated, and if there is any interference between the two components, Pro/Engineer will highlight the interfered positions. Figure 14 presents the result of the animation of model 1.
\n\t\t\t\tIn the assembly of model 1 and model 3 and their followers, there is no interference between the cam and its rollers when the cam rotates one revolution, while interferences occur in the assembly of model 2 and model 4. There are 10 positions of interference in the assembly of former, while there are a lot of positions of interferences for the latter. These interferences appear on both sides of the rib on the rise and return periods, where the curvature of working surfaces changes strongly, and can be seen in the graphic window (Figure 15). There are totally 1800 positions checked for a full revolution of the cam. The angle between two positions (called frames in Mechanism Design module) is 0.20. This value is similar to the increment of the input angle of the cam. In comparison with model 2 and model 4, the latter has bigger interference volumes. The result is that model 1 and model 3 can be accepted.
\n\t\t\t\tAlthough the interference does not occur between the cam surfaces of the acceptable models with their rollers, but there may have clearances between them. Thus, these clearances must be checked to ensure that they are small enough. If they are large, the errors of output angular displacements will be large and the model in this case may have to be eliminated. These clearances can be manually measured in assembly standard mode or in mechanism mode. The measuring result is that in one revolution of the cam the biggest clearances are on the rise and return periods and they are less than 0.2 micrometer for both models (Tuong & Pokorny, 2008). Obviously, these gaps also cause errors in the output angular displacements but these errors are very small and can be accepted.
\n\t\t\t\tIn this study, the four models above were created on a notebook with 1.86 GHz Core 2 Duo processor, 2GB RAM. It took only few minutes to create the pitch surface, the most time-consuming task, for the model of the first method (graphs-based method). Meanwhile, it took quite long with the methods that used 3D curves (method 3 and 4). The similar problem happened when performing the analysis running for checking interference. Therefore, the first method is the best choice when considering the modelling methods.
\n\t\t\t\tAnimation playback of model 1.
Interferences (in red colour) occur between components (model 4).
In our research, besides the example above, another example for modelling concave globoidal cam with indexing turret follower has also been done (Tuong & Pokorny, 2009). In that case study, the pitch surface-based modelling method was successfully used to create the cam. Some techniques which introduced above can be used for that case. However, the modelling procedure is much more complicated than the case of the concave globoidal cam with swinging roller follower. Figure 16 shows the animation playback of the concave globoidal cam with indexing turret follower.
\n\t\t\t\tAnimation playback of the concave globoidal cam with indexing turret follower.
In this study, four modelling methods are developed to create the concave globoidal cam. These methods are implemented in Pro/Engineer® Wildfire 2.0 using the same input data of a concave globoidal cam with an oscillating follower. After verifying the four models corresponding with the four methods, it can be said that the model which is created from the graphs-based method is the best one because it meets the required accuracy and the modelling time is short. This method is easy to conduct in Pro/Engineer, which is one of the most powerful CAD/CAM packages in industry. This is also a great potential for industry application. The case study presented here is a concrete example but the modelling methods and techniques can be applied for other spatial cams with cylindrical rollers when the angular input/output are known. The result of this study is very useful in terms of modelling and manufacturing globoidal cam.
\n\t\t\n\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t | \n\t\t\t\t\t\t\t | \n\t\t\t\t\t\t |
0.00 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 179.60 | \n\t\t\t\t\t\t\t44.99616011 | \n\t\t\t\t\t\t
0.20 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 179.80 | \n\t\t\t\t\t\t\t44.99904001 | \n\t\t\t\t\t\t
0.40 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 180.00 | \n\t\t\t\t\t\t\t45.00000000 | \n\t\t\t\t\t\t
0. 8 0 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 180.20 | \n\t\t\t\t\t\t\t44.99904001 | \n\t\t\t\t\t\t
0. 8 0 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 180.40 | \n\t\t\t\t\t\t\t44.99616011 | \n\t\t\t\t\t\t
1 . 0 0 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | … | \n\t\t\t\t\t\t\t… | \n\t\t\t\t\t\t
…. | \n\t\t\t\t\t\t\t… | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 213.00 | \n\t\t\t\t\t\t\t23.59739548 | \n\t\t\t\t\t\t
10 4 . 6 0 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 213.20 | \n\t\t\t\t\t\t\t23.39136475 | \n\t\t\t\t\t\t
10 4 . 8 0 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 213.40 | \n\t\t\t\t\t\t\t23.18530279 | \n\t\t\t\t\t\t
105.00 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 213.60 | \n\t\t\t\t\t\t\t22.97922791 | \n\t\t\t\t\t\t
105.20 | \n\t\t\t\t\t\t\t0.00000680 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 213.80 | \n\t\t\t\t\t\t\t22.77315844 | \n\t\t\t\t\t\t
105.40 | \n\t\t\t\t\t\t\t0.00005418 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 214.00 | \n\t\t\t\t\t\t\t22.56711268 | \n\t\t\t\t\t\t
105.60 | \n\t\t\t\t\t\t\t0.00018212 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 214.20 | \n\t\t\t\t\t\t\t22.36110896 | \n\t\t\t\t\t\t
105.80 | \n\t\t\t\t\t\t\t0.00042995 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 214.40 | \n\t\t\t\t\t\t\t22.15516558 | \n\t\t\t\t\t\t
106.00 | \n\t\t\t\t\t\t\t0.00083638 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 214.60 | \n\t\t\t\t\t\t\t21.94930085 | \n\t\t\t\t\t\t
106.20 | \n\t\t\t\t\t\t\t0.00143945 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | … | \n\t\t\t\t\t\t\t… | \n\t\t\t\t\t\t
106.40 | \n\t\t\t\t\t\t\t0.00227659 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 253.60 | \n\t\t\t\t\t\t\t0.00227659 | \n\t\t\t\t\t\t
106.60 | \n\t\t\t\t\t\t\t0.00338459 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 253.80 | \n\t\t\t\t\t\t\t0.00143945 | \n\t\t\t\t\t\t
106.80 | \n\t\t\t\t\t\t\t0.00479962 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 254.00 | \n\t\t\t\t\t\t\t0.00083638 | \n\t\t\t\t\t\t
… | \n\t\t\t\t\t\t\t… | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 254.20 | \n\t\t\t\t\t\t\t0.00042995 | \n\t\t\t\t\t\t
146.40 | \n\t\t\t\t\t\t\t22.97922791 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 254.40 | \n\t\t\t\t\t\t\t0.00018212 | \n\t\t\t\t\t\t
146.60 | \n\t\t\t\t\t\t\t23.18530279 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 254.60 | \n\t\t\t\t\t\t\t0.00005418 | \n\t\t\t\t\t\t
146.80 | \n\t\t\t\t\t\t\t23.39136475 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 254.80 | \n\t\t\t\t\t\t\t0.00000680 | \n\t\t\t\t\t\t
147.00 | \n\t\t\t\t\t\t\t23.59739548 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 255.00 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t
147.20 | \n\t\t\t\t\t\t\t23.80337666 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | … | \n\t\t\t\t\t\t\t… | \n\t\t\t\t\t\t
147.40 | \n\t\t\t\t\t\t\t24.00928999 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 359. 0 0 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t
147.60 | \n\t\t\t\t\t\t\t24.21511717 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 359. 2 0 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t
147.80 | \n\t\t\t\t\t\t\t24.42083990 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 3 59 . 4 0 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t
148.00 | \n\t\t\t\t\t\t\t24.62643991 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 359.60 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t
148.20 | \n\t\t\t\t\t\t\t24.83189893 | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 359.80 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t
… | \n\t\t\t\t\t\t\t… | \n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t | 360.00 | \n\t\t\t\t\t\t\t0.00000000 | \n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tTable 1. Example of some selected angular input/output displacements, unit: degree
The work upon which this paper is based is a part of MSM-4674788501 research program, grant from the Technical University of Liberec, Czech Republic.
\n\t\tIn unconventional oil and gas industry, there exists a significant granular flow process, which is known as the proppant transport [1]. It is necessary to pump high-strength granular materials such as ceramic particles and sand into the stimulated fracture networks with carrying fluid. Eventually after the flow-back of fluid, the granular materials remain in the fractures and fracture networks are efficiently propped, which contributes to a high conductivity for gas/oil exploitation. Therefore, it is important to reveal the physical mechanisms in the proppant transport process.
Essentially, proppant transport process is a two-phase flow problem constrained in a channel with various widths. In previous works, concentration transport approach was very popular for simulating the proppant transport. In the approach, proppant is considered as a continuum, and is quantitatively described using concentration. The motion of the particle phase is solved based on a concentration transport equation. This method is firstly established by Mobbs and Hammond [2]. They derived the governing equations for the fluid-particle mixture (i.e., slurry) by combining mass conservation laws of two phases and convection models. Then a Poisson equation for the fluid pressure is obtained. They proposed an important dimensionless number, that is, the Buoyancy number, to quantitatively describe the relative intensity of horizontal convection effect and the vertical settling effect. Their pioneering work is then adopted and extended in many later works. For example, Gadde and Sharma [3] and Gu and Mohanty [4] extended this framework by considering the effects of fracture propagation. Wang et al. [5] introduced a blocking function in order to consider the proppant bridging effect. Dontsov and Peirce [6] utilized a more accurate velocity retardation model based on their theoretical analysis. Roostaei et al. [7] applied the WENO (weighted essentially non-oscillation) scheme to solve the concentration transport equation, which greatly reduces the numerical diffusion.
The MP-PIC method [8, 9] is another numerical method for simulating large-scale fluid-particle coupling system, which is popular in chemical engineering. In the MP-PIC method, fluid motion is governed by the volume-averaged Navier-Stokes equation, and particle motion is solved using the Newton’s second law under the Lagrangian framework, which is different from those in the concentration approach. Due to its Lagrangian feature and high fidelity, the MP-PIC method is also shown to be a powerful tool for simulating proppant transport process.
In this work, the two above numerical methods are both applied in simulating the proppant transport process. Though the two numerical methods are built under different frameworks, there exist both similarities and differences between them. The hidden facts are revealed based on the analysis of the governing equation sets, as well as the numerical results. The remaining contents of this work are organized as follows. In Section 2, basic governing equation sets of the two methods are demonstrated, and relationship between the two methods are discussed. In Section 3, several numerical cases are designed to illustrate the performance of the two methods, and the numerical results are then discussed. Finally, conclusions are drawn in the Section 4.
Assume that there exists only one kind of proppant (same density and size, or mono-disperse) in the fracture and the particle phase is well distributed so that in the large scale we can take the derivative of the particle concentration in most regions (except discontinuity), and the particle and fluid phase are both incompressible. Then we have following unknown variables: fluid velocity
Let us start from the continuity equation. Figure 1 shows the fluxes and accumulation in a control volume. It is clear that for the particle phase we have the mass balance equation:
Control volume in concentration transport approach.
where w is the fracture width. Then it is trivial to obtain the differential form [2]:
Similarly, we have the mass balance equation for fluid phase:
Considering fluid leak-off, it is trivial to add a source term in the RHS:
where
In large-scale cases, we assume that in the horizontal direction, the velocities of the two phases are the same (homogeneous slurry flow), and in the vertical direction, the particle phase velocity differs from the fluid phase due to particle settling. Then we have the following formula:
where
Using Eqs. (2) and (4), we can obtain the fluid/particle mixture (slurry) continuity equation.
where
Eq. (6) is necessary for solving fluid pressure and it is illustrated below. As we know, for pure Newtonian fluid, we have the constitutive laws in which viscosity is a significant parameter. In viscous case (low Re number), based on the Poiseuille’s Law, we can derive the relationship between the pressure gradient and average velocity in a channel/fracture:
where
In the case of fluid/particle mixture, we also expect there exists a similar relationship between fluid pressure and slurry velocity. There are many previous literatures including experimental and numerical works revealing this relationship. It is well known that the apparent viscosity of the mixture is higher than that of the pure fluid and a formula similar to Eq. (7) can be obtained introducing the effective viscosity of the mixture [7]:
where
By substituting Eq. (8) into Eq. (6), we get the following pressure Eq. (7):
If the fracture width does not vary with time, then the time derivative vanishes, with the pressure Poisson equation remaining, and the sand concentration
The MP-PIC method is an Eulerian-Lagrangian method, in which fluid motion is solved in the Eulerian grids and particle motion is solved under the Lagrangian framework. The governing equation of fluid motion reads [10]:
where w is the fracture width,
In the MP-PIC method, the particle phase is discretized into parcels, and every parcel represents several physical particles, which possess the same properties such as density and size, and also similar kinetic behavior such as the velocity and acceleration. Parcel motion is governed by the Newton’s second law listed as follows:
where
First let us summarize the governing equations of the two approaches.
Concentration transport approach:
MP-PIC approach:
In Eq. (13), we need to introduce models for settling velocity
Next we will discuss the similarity and difference between these two equation sets, which are denoted as set I and set II, respectively:
Fluid part: it is clear that in set II unsteady and convection/inertial terms are considered. Set I is suitable for homogeneous slurry flow, which indicates that particles settle pretty slowly and Reynolds number is low. In slick water cases, set II is preferred. Actually set II shall converge into set I in low Re number cases. In steady cases, the unsteady terms vanish and the fluid-particle interaction term converges into additional gravity force of particle phase, then the second equation in set II is simplified as:
If the term
Particle part: obviously we solve particle phase motion under Eulerian framework in set I while under Lagrangian framework in set II. Density/size distribution is easier to be considered in set II. In set I we directly assign a settling velocity for the particle phase while in set II we can resolve the settling history with the drag relaxation term if the time step is set to be small enough. The terminal velocity in set II is determined by which drag force model is utilized. Both of the settling velocity model in set I and drag force model in set II are modifications of Stokes settling theoretical results. Also unsteady terms including fluid pressure and viscous stress effects are considered in set II.
In both of the two 2D large-scale equation sets, models are necessary for closure issues and they cannot exactly describe the full-scale fluid/particle behavior. “Large scale” has two meanings: large time scale and large spatial scale. Different physical mechanisms play significant roles in different scales. For the time scales, p-p collision occurs in the time scale of “μs,” f-p drag occurs in the time scale of “ms,” fluid leak-off and fracture width change have significant effects in the time scale of “s” or “min.” For the spatial scales, fluid viscous force dominates in the Kolmogorov length scale (mm), gravity convection dominates in the length scale of “m.” We expect that in our 2D large-scale models, we can capture the large-scale fluid/particle behavior. However, small-scale fluid/particle interactions shall affect the large-scale phenomena.
Using 3D DNS (direct numerical simulation) we can obtain the full-scale details; however, due to computational limits simulation time at most reaches several minutes and simulation length at most reaches 1 dm. Though it is not possible to perform 3D DNS even for an experimental-scale case, useful models can be extracted from the DNS data, for example effective viscosity, settling velocity, retardation factor etc.
In this work, Barree and Conway’s [11] effective viscosity model is utilized to calculate slurry viscosity for the concentration transport approach and calculate wall friction force for the MP-PIC method, which is expressed as follows:
where
Besides, Wen and Yu’s drag force model [12] is utilized for calculating the fluid-particle coupling drag force for the MP-PIC method and determining particle settling velocity for the concentration transport approach, which is expressed as follows:
where
Numerical simulation is performed in a rectangle domain as shown in Figure 2. The left side of the domain is set as inlet. Proppant is uniformly injected from the whole inlet and proppant concentration is set as 20%. Here the proppant concentration means the volume ratio of particles to total volume of fluid/particle mixture. The right side of the domain is set as outlet. The upper and bottom sides of the rectangle domain are set as the non-flow boundary. Particle deposition mechanisms are different in these two methods. In the concentration transport approach, if proppant concentration reaches the close packing limit, particle settling velocity is set to be approaching zero, and it is easy to implement the non-flow condition for a Eulerian approach. In the MP-PIC method, if proppant concentration reaches the close packing limit, additional forces due to particle stress gradient are exerted on parcels to make sure these parcels shall move away from the high-concentration region. When parcels move across the non-flow boundary, the displacements of these parcels are modified following a bounce-back way.
A sketch for the numerical simulation domain.
Parameters used in the simulation are listed in Table 1. Cases with different fluid viscosities, that is, 1, 10, and 100 cP are considered in this section. Because characteristic length is 0.005 m (fracture width) and characteristic velocity is 0.2 m/s (inlet velocity), the Reynolds numbers in these cases are 1000, 100, and 10 respectively.
Parameter | Value | Parameter | Value |
---|---|---|---|
Fluid density | 1000 kg/m3 | Particle density | 2500 kg/m3 |
Fluid viscosity | 1 and 10 and 100 cP | Particle diameter | 0.6 mm |
Time-step | Simulation time | 4 s | |
Inlet velocity | 0.2 m/s | Inlet concentration | 20% |
Domain size | Mesh size |
Parameters for simulating proppant transport.
Figures 3–5 show the numerical results of three different Reynolds number cases of two methods. The results are contoured by the volume fraction of particle (denoted as “vfp”), or the proppant concentration. Here we denote the high Reynolds number case as case I, the moderate Reynolds number case as case II, and the low Reynolds number case as case III respectively.
Simulation results of high Reynolds number case (Re = 1000). (a)–(d) are the concentration transport results at time = 1, 2, 3, and 4 s respectively, and (e)–(h) are the MP-PIC results at time = 1, 2, 3, and 4 s respectively.
Simulation results of moderate Reynolds number case (Re = 100). (a)–(d) are the concentration transport results at time = 1, 2, 3, and 4 s respectively, and (e)–(h) are the MP-PIC results at time = 1, 2, 3, and 4 s respectively.
Simulation results of low Reynolds number case (Re = 10). (a)–(d) are the concentration transport results at time = 1, 2, 3, and 4 s respectively, and (e)–(h) are the MP-PIC results at time = 1, 2, 3, and 4 s respectively.
In case I the viscosity of carrying fluid is very low, that is, 1 cp, which indicates a poor capability of proppant transport. From Figure 3, it is clear that both of the two numerical methods illustrate the packing process during the transport process. In the figure, blue, white, and red regions indicate the pure fluid, suspending slurry, and sandbank regions respectively. In case II, settling behavior of proppant is weaker than that of case I, and instead gravity convection of the slurry front in the vertical direction is obvious as shown in Figure 4. In case III, it is obvious from Figure 5 that proppant settling behavior is hard to recognize and gravity convection is much weaker than that of case II.
By comparing the results at different Reynolds numbers, it can be summarized that as the slurry is injected into the domain, there are several significant mechanisms that determine the eventual proppant distribution listed as follows.
The first mechanism is proppant settling. Proppant settling is due to the net gravity force of the proppant if particle density is larger than the fluid density, and the terminal velocity of proppant is determined by the particle Reynolds number and particle volume fraction. According to the Wen and Yu’s drag force model, it is trivial to obtain the settling velocities of proppant in the above three tests, and they are 53.2, 11.8, and 1.28 mm/s, respectively. Therefore, within a same horizontal transport distance, the level of slurry-pure water interface declines more dramatically in case I compared to the other two cases with lower Reynolds numbers.
The second one is gravity convection. In case II and case III, proppant settling can be ignored compared to the inlet velocity, however the slurry fronts in these two cases still evolve and both trend from vertical direction to inclined direction. This is because of the horizontal pressure gradient on the slurry front due to the difference between slurry and pure fluid, which provides a driving force and keeps slurry on the bottom penetrating into the pure fluid region. This mechanism is then intuitively described as gravity convection. Gravity convection in case III is much weaker than that in case II. Though the horizontal pressure gradients on the slurry front are the same in these two cases, fluid viscosity is greater in case III, which leads to a smaller channel permeability for slurry flows. Therefore, the penetration velocity in case III is much smaller than that in case II. In case I, gravity convection also plays a significant role. According to the ratio of inlet velocity and proppant settling velocity, that is, about 4, without gravity convection slurry front is expected to be exact the diagonal line of the domain. However, numerical results of both methods show that the suspending region is far below the diagonal line, which indicates that fluid velocity field is greatly changed due to gravity convection compared to a uniform flow. Above all, gravity convection can be considered as a global effect reflecting the density difference between slurry and pure fluid, whereas proppant settling represents a local effect reflecting the density difference between proppant particle and pure fluid.
The third one is proppant packing. The two prior mechanisms affect the distribution of slurry suspending region, and proppant packing shall affect the distribution of sandbank. In case I, as time evolves proppant concentration increases at the bottom of the simulation domain. When proppant concentration reaches a maximum value, that is, close to the packing state, particle-particle interactions and particle-wall interactions become more frequent. Then, the early formed sandbank stays unmovable, and the fluid velocity also dramatically decreases in this region due to the fluid-particle coupling and particle-particle/wall damping effects.
By comparing the numerical results of two different methods based on the above mechanisms, similarities and differences between the two methods discussed in Section 2.3 are verified.
Firstly, in case III it is obvious that numerical results of methods are almost the same with each other. In case III, Reynolds number is pretty low and the fluid motion is dominated by the viscous mechanism. The slurry flow is approximately plug flow. Secondly, in case II of moderate Reynolds number, numerical results of concentration transport approach show that the gravity convection is a bit severe than those of MP-PIC method. However, transport patterns of these two methods are in general similar. Quantitatively, the relative length of top and bottom slurry fronts at the end of simulation time is 0.5 and 0.4 m, respectively. Thirdly, in case I, numerical results of two methods differ a lot from each other. For the slurry suspending region, the covering area of the MP-PIC results is obviously much larger than those of concentration transport approach. This is mainly because the transient term and convection term in the fluid governing equation are ignored in the concentration approach, and these two mechanisms play significant roles in low viscous or high Reynolds number cases. It is clear that losses of these two mechanisms shall under-estimate the transport capability when utilizing the concentration transport approach. Besides, sandbank packing process in the concentration transport results also differ a lot from that in the MP-PIC results, including the slopes of upstream and downstream sandbank region. This is because particle-particle interaction is considered in the MP-PIC method in some way, while it is not considered in the concentration transport approach.
It is worth noting here that in this work the fifth order WENO (weighted essentially non-oscillation) scheme is adopted for solving the concentration transport equation, thus the effect of numerical diffusion of concentration transport approach can be considered insignificant, and differences between the numerical results of two methods can exactly reflect the effects of different modeling strategy on proppant transport. Above all, both methods can precisely capture the proppant settling mechanism when the same drag force model is adopted in both methods, and concentration transport approach can capture the gravity convection mechanisms precisely when Reynolds number is smaller than 100. However, proppant packing mechanism is not captured very well in the concentration approach.
In this work, two numerical methods are adopted to simulate proppant transport: the concentration transport approach and the MP-PIC method. The first one is a typical Eulerian-Eulerian method and the second one is a typical Eulerian-Lagrangian method. With full discussions on their frameworks and comparisons between the numerical results, the following conclusions are then obtained:
From the view of pure horizontal proppant advection, numerical diffusion can be insignificant in the concentration transport approach if high-order scheme like WENO scheme is adopted, and the interfaces between slurry front and pure fluid can be clearly captured.
When fluid Reynolds number is smaller than 100, assumptions of ignoring velocity convection term and transient term for fluid governing equation adopted in the concentration transport approach are reasonable, and numerical results of both methods show similar transport patterns.
When fluid Reynolds number reaches 1000, that is, in the low viscous cases, numerical experiments prove that the concentration transport approach shows a low fidelity for capturing both the slurry suspending region and the sandbank packing process.
Generally, the more physical mechanisms, including particle-particle/wall interaction and fluid-particle interaction, accurately considered in a numerical framework, the better a simulator performs on capturing proppant transport behaviors.
This work is funded by the National Natural Science Foundation of China (nos. U1730111, 11972088, 91852207), the State Key Laboratory of Explosive Science and Technology (no. QNKT19-05), and the National Science and Technology Major Project of China (Grant no. 2017ZX05039-005).
IntechOpen’s team of Scientific Advisors supports the publishing team by providing editorial and academic input and ensuring the highest quality output of free peer-reviewed articles. The Boards consist of independent external collaborators who assist us on a voluntary basis. Their input includes advising on new topics within their field, proposing potential expert collaborators and reviewing book publishing proposals if required. Board members are experts who cover major STEM and HSS fields. All are trusted IntechOpen collaborators and Academic Editors, ensuring that the needs of the scientific community are met.
",metaTitle:"STM Publishing and Free Peer Reviewed Articles | IntechOpen",metaDescription:"IntechOpen’s scientific advisors support the STM publishing team by offering their editorial input, ensuring a consistent output of free peer reviewed articles.",metaKeywords:null,canonicalURL:"scientific-advisors",contentRaw:'[{"type":"htmlEditorComponent","content":"\\n"}]'},components:[{type:"htmlEditorComponent",content:'
\n'}]},successStories:{items:[]},authorsAndEditors:{filterParams:{sort:"featured,name"},profiles:[{id:"6700",title:"Dr.",name:"Abbass A.",middleName:null,surname:"Hashim",slug:"abbass-a.-hashim",fullName:"Abbass A. Hashim",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/6700/images/1864_n.jpg",biography:"Currently I am carrying out research in several areas of interest, mainly covering work on chemical and bio-sensors, semiconductor thin film device fabrication and characterisation.\nAt the moment I have very strong interest in radiation environmental pollution and bacteriology treatment. The teams of researchers are working very hard to bring novel results in this field. I am also a member of the team in charge for the supervision of Ph.D. students in the fields of development of silicon based planar waveguide sensor devices, study of inelastic electron tunnelling in planar tunnelling nanostructures for sensing applications and development of organotellurium(IV) compounds for semiconductor applications. I am a specialist in data analysis techniques and nanosurface structure. I have served as the editor for many books, been a member of the editorial board in science journals, have published many papers and hold many patents.",institutionString:null,institution:{name:"Sheffield Hallam University",country:{name:"United Kingdom"}}},{id:"54525",title:"Prof.",name:"Abdul Latif",middleName:null,surname:"Ahmad",slug:"abdul-latif-ahmad",fullName:"Abdul Latif Ahmad",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"20567",title:"Prof.",name:"Ado",middleName:null,surname:"Jorio",slug:"ado-jorio",fullName:"Ado Jorio",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Universidade Federal de Minas Gerais",country:{name:"Brazil"}}},{id:"47940",title:"Dr.",name:"Alberto",middleName:null,surname:"Mantovani",slug:"alberto-mantovani",fullName:"Alberto Mantovani",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"12392",title:"Mr.",name:"Alex",middleName:null,surname:"Lazinica",slug:"alex-lazinica",fullName:"Alex Lazinica",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/12392/images/7282_n.png",biography:"Alex Lazinica is the founder and CEO of IntechOpen. After obtaining a Master's degree in Mechanical Engineering, he continued his PhD studies in Robotics at the Vienna University of Technology. Here he worked as a robotic researcher with the university's Intelligent Manufacturing Systems Group as well as a guest researcher at various European universities, including the Swiss Federal Institute of Technology Lausanne (EPFL). During this time he published more than 20 scientific papers, gave presentations, served as a reviewer for major robotic journals and conferences and most importantly he co-founded and built the International Journal of Advanced Robotic Systems- world's first Open Access journal in the field of robotics. Starting this journal was a pivotal point in his career, since it was a pathway to founding IntechOpen - Open Access publisher focused on addressing academic researchers needs. Alex is a personification of IntechOpen key values being trusted, open and entrepreneurial. Today his focus is on defining the growth and development strategy for the company.",institutionString:null,institution:{name:"TU Wien",country:{name:"Austria"}}},{id:"19816",title:"Prof.",name:"Alexander",middleName:null,surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/19816/images/1607_n.jpg",biography:"Alexander I. Kokorin: born: 1947, Moscow; DSc., PhD; Principal Research Fellow (Research Professor) of Department of Kinetics and Catalysis, N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow.\r\nArea of research interests: physical chemistry of complex-organized molecular and nanosized systems, including polymer-metal complexes; the surface of doped oxide semiconductors. He is an expert in structural, absorptive, catalytic and photocatalytic properties, in structural organization and dynamic features of ionic liquids, in magnetic interactions between paramagnetic centers. The author or co-author of 3 books, over 200 articles and reviews in scientific journals and books. He is an actual member of the International EPR/ESR Society, European Society on Quantum Solar Energy Conversion, Moscow House of Scientists, of the Board of Moscow Physical Society.",institutionString:null,institution:{name:"Semenov Institute of Chemical Physics",country:{name:"Russia"}}},{id:"62389",title:"PhD.",name:"Ali Demir",middleName:null,surname:"Sezer",slug:"ali-demir-sezer",fullName:"Ali Demir Sezer",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/62389/images/3413_n.jpg",biography:"Dr. Ali Demir Sezer has a Ph.D. from Pharmaceutical Biotechnology at the Faculty of Pharmacy, University of Marmara (Turkey). He is the member of many Pharmaceutical Associations and acts as a reviewer of scientific journals and European projects under different research areas such as: drug delivery systems, nanotechnology and pharmaceutical biotechnology. Dr. Sezer is the author of many scientific publications in peer-reviewed journals and poster communications. Focus of his research activity is drug delivery, physico-chemical characterization and biological evaluation of biopolymers micro and nanoparticles as modified drug delivery system, and colloidal drug carriers (liposomes, nanoparticles etc.).",institutionString:null,institution:{name:"Marmara University",country:{name:"Turkey"}}},{id:"61051",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"100762",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"St David's Medical Center",country:{name:"United States of America"}}},{id:"107416",title:"Dr.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Texas Cardiac Arrhythmia",country:{name:"United States of America"}}},{id:"64434",title:"Dr.",name:"Angkoon",middleName:null,surname:"Phinyomark",slug:"angkoon-phinyomark",fullName:"Angkoon Phinyomark",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/64434/images/2619_n.jpg",biography:"My name is Angkoon Phinyomark. I received a B.Eng. degree in Computer Engineering with First Class Honors in 2008 from Prince of Songkla University, Songkhla, Thailand, where I received a Ph.D. degree in Electrical Engineering. My research interests are primarily in the area of biomedical signal processing and classification notably EMG (electromyography signal), EOG (electrooculography signal), and EEG (electroencephalography signal), image analysis notably breast cancer analysis and optical coherence tomography, and rehabilitation engineering. I became a student member of IEEE in 2008. During October 2011-March 2012, I had worked at School of Computer Science and Electronic Engineering, University of Essex, Colchester, Essex, United Kingdom. In addition, during a B.Eng. I had been a visiting research student at Faculty of Computer Science, University of Murcia, Murcia, Spain for three months.\n\nI have published over 40 papers during 5 years in refereed journals, books, and conference proceedings in the areas of electro-physiological signals processing and classification, notably EMG and EOG signals, fractal analysis, wavelet analysis, texture analysis, feature extraction and machine learning algorithms, and assistive and rehabilitative devices. I have several computer programming language certificates, i.e. Sun Certified Programmer for the Java 2 Platform 1.4 (SCJP), Microsoft Certified Professional Developer, Web Developer (MCPD), Microsoft Certified Technology Specialist, .NET Framework 2.0 Web (MCTS). I am a Reviewer for several refereed journals and international conferences, such as IEEE Transactions on Biomedical Engineering, IEEE Transactions on Industrial Electronics, Optic Letters, Measurement Science Review, and also a member of the International Advisory Committee for 2012 IEEE Business Engineering and Industrial Applications and 2012 IEEE Symposium on Business, Engineering and Industrial Applications.",institutionString:null,institution:{name:"Joseph Fourier University",country:{name:"France"}}},{id:"55578",title:"Dr.",name:"Antonio",middleName:null,surname:"Jurado-Navas",slug:"antonio-jurado-navas",fullName:"Antonio Jurado-Navas",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/55578/images/4574_n.png",biography:"Antonio Jurado-Navas received the M.S. degree (2002) and the Ph.D. degree (2009) in Telecommunication Engineering, both from the University of Málaga (Spain). He first worked as a consultant at Vodafone-Spain. From 2004 to 2011, he was a Research Assistant with the Communications Engineering Department at the University of Málaga. In 2011, he became an Assistant Professor in the same department. From 2012 to 2015, he was with Ericsson Spain, where he was working on geo-location\ntools for third generation mobile networks. Since 2015, he is a Marie-Curie fellow at the Denmark Technical University. His current research interests include the areas of mobile communication systems and channel modeling in addition to atmospheric optical communications, adaptive optics and statistics",institutionString:null,institution:{name:"University of Malaga",country:{name:"Spain"}}}],filtersByRegion:[{group:"region",caption:"North America",value:1,count:5703},{group:"region",caption:"Middle and South America",value:2,count:5174},{group:"region",caption:"Africa",value:3,count:1690},{group:"region",caption:"Asia",value:4,count:10246},{group:"region",caption:"Australia and Oceania",value:5,count:889},{group:"region",caption:"Europe",value:6,count:15653}],offset:12,limit:12,total:117317},chapterEmbeded:{data:{}},editorApplication:{success:null,errors:{}},ofsBooks:{filterParams:{topicId:"17"},books:[],filtersByTopic:[{group:"topic",caption:"Agricultural and Biological Sciences",value:5,count:9},{group:"topic",caption:"Biochemistry, Genetics and Molecular Biology",value:6,count:14},{group:"topic",caption:"Business, Management and Economics",value:7,count:2},{group:"topic",caption:"Chemistry",value:8,count:6},{group:"topic",caption:"Computer and Information Science",value:9,count:10},{group:"topic",caption:"Earth and Planetary Sciences",value:10,count:4},{group:"topic",caption:"Engineering",value:11,count:16},{group:"topic",caption:"Environmental Sciences",value:12,count:2},{group:"topic",caption:"Immunology and Microbiology",value:13,count:4},{group:"topic",caption:"Materials Science",value:14,count:5},{group:"topic",caption:"Mathematics",value:15,count:1},{group:"topic",caption:"Medicine",value:16,count:57},{group:"topic",caption:"Neuroscience",value:18,count:1},{group:"topic",caption:"Pharmacology, Toxicology and Pharmaceutical Science",value:19,count:5},{group:"topic",caption:"Physics",value:20,count:2},{group:"topic",caption:"Psychology",value:21,count:3},{group:"topic",caption:"Robotics",value:22,count:1},{group:"topic",caption:"Social Sciences",value:23,count:3},{group:"topic",caption:"Technology",value:24,count:1},{group:"topic",caption:"Veterinary Medicine and Science",value:25,count:2}],offset:12,limit:12,total:0},popularBooks:{featuredBooks:[{type:"book",id:"7802",title:"Modern Slavery and Human Trafficking",subtitle:null,isOpenForSubmission:!1,hash:"587a0b7fb765f31cc98de33c6c07c2e0",slug:"modern-slavery-and-human-trafficking",bookSignature:"Jane Reeves",coverURL:"https://cdn.intechopen.com/books/images_new/7802.jpg",editors:[{id:"211328",title:"Prof.",name:"Jane",middleName:null,surname:"Reeves",slug:"jane-reeves",fullName:"Jane Reeves"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9961",title:"Data Mining",subtitle:"Methods, Applications and Systems",isOpenForSubmission:!1,hash:"ed79fb6364f2caf464079f94a0387146",slug:"data-mining-methods-applications-and-systems",bookSignature:"Derya Birant",coverURL:"https://cdn.intechopen.com/books/images_new/9961.jpg",editors:[{id:"15609",title:"Dr.",name:"Derya",middleName:null,surname:"Birant",slug:"derya-birant",fullName:"Derya Birant"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8545",title:"Animal Reproduction in Veterinary Medicine",subtitle:null,isOpenForSubmission:!1,hash:"13aaddf5fdbbc78387e77a7da2388bf6",slug:"animal-reproduction-in-veterinary-medicine",bookSignature:"Faruk Aral, Rita Payan-Carreira and Miguel Quaresma",coverURL:"https://cdn.intechopen.com/books/images_new/8545.jpg",editors:[{id:"25600",title:"Prof.",name:"Faruk",middleName:null,surname:"Aral",slug:"faruk-aral",fullName:"Faruk Aral"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9157",title:"Neurodegenerative Diseases",subtitle:"Molecular Mechanisms and Current Therapeutic Approaches",isOpenForSubmission:!1,hash:"bc8be577966ef88735677d7e1e92ed28",slug:"neurodegenerative-diseases-molecular-mechanisms-and-current-therapeutic-approaches",bookSignature:"Nagehan Ersoy Tunalı",coverURL:"https://cdn.intechopen.com/books/images_new/9157.jpg",editors:[{id:"82778",title:"Ph.D.",name:"Nagehan",middleName:null,surname:"Ersoy Tunalı",slug:"nagehan-ersoy-tunali",fullName:"Nagehan Ersoy Tunalı"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8686",title:"Direct Torque Control Strategies of Electrical Machines",subtitle:null,isOpenForSubmission:!1,hash:"b6ad22b14db2b8450228545d3d4f6b1a",slug:"direct-torque-control-strategies-of-electrical-machines",bookSignature:"Fatma Ben Salem",coverURL:"https://cdn.intechopen.com/books/images_new/8686.jpg",editors:[{id:"295623",title:"Associate Prof.",name:"Fatma",middleName:null,surname:"Ben Salem",slug:"fatma-ben-salem",fullName:"Fatma Ben Salem"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7434",title:"Molecular Biotechnology",subtitle:null,isOpenForSubmission:!1,hash:"eceede809920e1ec7ecadd4691ede2ec",slug:"molecular-biotechnology",bookSignature:"Sergey Sedykh",coverURL:"https://cdn.intechopen.com/books/images_new/7434.jpg",editors:[{id:"178316",title:"Ph.D.",name:"Sergey",middleName:null,surname:"Sedykh",slug:"sergey-sedykh",fullName:"Sergey Sedykh"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9208",title:"Welding",subtitle:"Modern Topics",isOpenForSubmission:!1,hash:"7d6be076ccf3a3f8bd2ca52d86d4506b",slug:"welding-modern-topics",bookSignature:"Sadek Crisóstomo Absi Alfaro, Wojciech Borek and Błażej Tomiczek",coverURL:"https://cdn.intechopen.com/books/images_new/9208.jpg",editors:[{id:"65292",title:"Prof.",name:"Sadek Crisostomo Absi",middleName:"C. Absi",surname:"Alfaro",slug:"sadek-crisostomo-absi-alfaro",fullName:"Sadek Crisostomo Absi Alfaro"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7831",title:"Sustainability in Urban Planning and Design",subtitle:null,isOpenForSubmission:!1,hash:"c924420492c8c2c9751e178d025f4066",slug:"sustainability-in-urban-planning-and-design",bookSignature:"Amjad Almusaed, Asaad Almssad and Linh Truong - Hong",coverURL:"https://cdn.intechopen.com/books/images_new/7831.jpg",editors:[{id:"110471",title:"Dr.",name:"Amjad",middleName:"Zaki",surname:"Almusaed",slug:"amjad-almusaed",fullName:"Amjad Almusaed"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9343",title:"Trace Metals in the Environment",subtitle:"New Approaches and Recent Advances",isOpenForSubmission:!1,hash:"ae07e345bc2ce1ebbda9f70c5cd12141",slug:"trace-metals-in-the-environment-new-approaches-and-recent-advances",bookSignature:"Mario Alfonso Murillo-Tovar, Hugo Saldarriaga-Noreña and Agnieszka Saeid",coverURL:"https://cdn.intechopen.com/books/images_new/9343.jpg",editors:[{id:"255959",title:"Dr.",name:"Mario Alfonso",middleName:null,surname:"Murillo-Tovar",slug:"mario-alfonso-murillo-tovar",fullName:"Mario Alfonso Murillo-Tovar"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9139",title:"Topics in Primary Care Medicine",subtitle:null,isOpenForSubmission:!1,hash:"ea774a4d4c1179da92a782e0ae9cde92",slug:"topics-in-primary-care-medicine",bookSignature:"Thomas F. Heston",coverURL:"https://cdn.intechopen.com/books/images_new/9139.jpg",editors:[{id:"217926",title:"Dr.",name:"Thomas F.",middleName:null,surname:"Heston",slug:"thomas-f.-heston",fullName:"Thomas F. Heston"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9839",title:"Outdoor Recreation",subtitle:"Physiological and Psychological Effects on Health",isOpenForSubmission:!1,hash:"5f5a0d64267e32567daffa5b0c6a6972",slug:"outdoor-recreation-physiological-and-psychological-effects-on-health",bookSignature:"Hilde G. Nielsen",coverURL:"https://cdn.intechopen.com/books/images_new/9839.jpg",editors:[{id:"158692",title:"Ph.D.",name:"Hilde G.",middleName:null,surname:"Nielsen",slug:"hilde-g.-nielsen",fullName:"Hilde G. Nielsen"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8697",title:"Virtual Reality and Its Application in Education",subtitle:null,isOpenForSubmission:!1,hash:"ee01b5e387ba0062c6b0d1e9227bda05",slug:"virtual-reality-and-its-application-in-education",bookSignature:"Dragan Cvetković",coverURL:"https://cdn.intechopen.com/books/images_new/8697.jpg",editors:[{id:"101330",title:"Dr.",name:"Dragan",middleName:"Mladen",surname:"Cvetković",slug:"dragan-cvetkovic",fullName:"Dragan Cvetković"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}}],offset:12,limit:12,total:5146},hotBookTopics:{hotBooks:[],offset:0,limit:12,total:null},publish:{},publishingProposal:{success:null,errors:{}},books:{featuredBooks:[{type:"book",id:"7802",title:"Modern Slavery and Human Trafficking",subtitle:null,isOpenForSubmission:!1,hash:"587a0b7fb765f31cc98de33c6c07c2e0",slug:"modern-slavery-and-human-trafficking",bookSignature:"Jane Reeves",coverURL:"https://cdn.intechopen.com/books/images_new/7802.jpg",editors:[{id:"211328",title:"Prof.",name:"Jane",middleName:null,surname:"Reeves",slug:"jane-reeves",fullName:"Jane Reeves"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9961",title:"Data Mining",subtitle:"Methods, Applications and Systems",isOpenForSubmission:!1,hash:"ed79fb6364f2caf464079f94a0387146",slug:"data-mining-methods-applications-and-systems",bookSignature:"Derya Birant",coverURL:"https://cdn.intechopen.com/books/images_new/9961.jpg",editors:[{id:"15609",title:"Dr.",name:"Derya",middleName:null,surname:"Birant",slug:"derya-birant",fullName:"Derya Birant"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8545",title:"Animal Reproduction in Veterinary Medicine",subtitle:null,isOpenForSubmission:!1,hash:"13aaddf5fdbbc78387e77a7da2388bf6",slug:"animal-reproduction-in-veterinary-medicine",bookSignature:"Faruk Aral, Rita Payan-Carreira and Miguel Quaresma",coverURL:"https://cdn.intechopen.com/books/images_new/8545.jpg",editors:[{id:"25600",title:"Prof.",name:"Faruk",middleName:null,surname:"Aral",slug:"faruk-aral",fullName:"Faruk Aral"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9157",title:"Neurodegenerative Diseases",subtitle:"Molecular Mechanisms and Current Therapeutic Approaches",isOpenForSubmission:!1,hash:"bc8be577966ef88735677d7e1e92ed28",slug:"neurodegenerative-diseases-molecular-mechanisms-and-current-therapeutic-approaches",bookSignature:"Nagehan Ersoy Tunalı",coverURL:"https://cdn.intechopen.com/books/images_new/9157.jpg",editors:[{id:"82778",title:"Ph.D.",name:"Nagehan",middleName:null,surname:"Ersoy Tunalı",slug:"nagehan-ersoy-tunali",fullName:"Nagehan Ersoy Tunalı"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"8686",title:"Direct Torque Control Strategies of Electrical Machines",subtitle:null,isOpenForSubmission:!1,hash:"b6ad22b14db2b8450228545d3d4f6b1a",slug:"direct-torque-control-strategies-of-electrical-machines",bookSignature:"Fatma Ben Salem",coverURL:"https://cdn.intechopen.com/books/images_new/8686.jpg",editors:[{id:"295623",title:"Associate Prof.",name:"Fatma",middleName:null,surname:"Ben Salem",slug:"fatma-ben-salem",fullName:"Fatma Ben Salem"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7434",title:"Molecular Biotechnology",subtitle:null,isOpenForSubmission:!1,hash:"eceede809920e1ec7ecadd4691ede2ec",slug:"molecular-biotechnology",bookSignature:"Sergey Sedykh",coverURL:"https://cdn.intechopen.com/books/images_new/7434.jpg",editors:[{id:"178316",title:"Ph.D.",name:"Sergey",middleName:null,surname:"Sedykh",slug:"sergey-sedykh",fullName:"Sergey Sedykh"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9208",title:"Welding",subtitle:"Modern Topics",isOpenForSubmission:!1,hash:"7d6be076ccf3a3f8bd2ca52d86d4506b",slug:"welding-modern-topics",bookSignature:"Sadek Crisóstomo Absi Alfaro, Wojciech Borek and Błażej Tomiczek",coverURL:"https://cdn.intechopen.com/books/images_new/9208.jpg",editors:[{id:"65292",title:"Prof.",name:"Sadek Crisostomo Absi",middleName:"C. Absi",surname:"Alfaro",slug:"sadek-crisostomo-absi-alfaro",fullName:"Sadek Crisostomo Absi Alfaro"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"7831",title:"Sustainability in Urban Planning and Design",subtitle:null,isOpenForSubmission:!1,hash:"c924420492c8c2c9751e178d025f4066",slug:"sustainability-in-urban-planning-and-design",bookSignature:"Amjad Almusaed, Asaad Almssad and Linh Truong - Hong",coverURL:"https://cdn.intechopen.com/books/images_new/7831.jpg",editors:[{id:"110471",title:"Dr.",name:"Amjad",middleName:"Zaki",surname:"Almusaed",slug:"amjad-almusaed",fullName:"Amjad Almusaed"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9343",title:"Trace Metals in the Environment",subtitle:"New Approaches and Recent Advances",isOpenForSubmission:!1,hash:"ae07e345bc2ce1ebbda9f70c5cd12141",slug:"trace-metals-in-the-environment-new-approaches-and-recent-advances",bookSignature:"Mario Alfonso Murillo-Tovar, Hugo Saldarriaga-Noreña and Agnieszka Saeid",coverURL:"https://cdn.intechopen.com/books/images_new/9343.jpg",editors:[{id:"255959",title:"Dr.",name:"Mario Alfonso",middleName:null,surname:"Murillo-Tovar",slug:"mario-alfonso-murillo-tovar",fullName:"Mario Alfonso Murillo-Tovar"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}},{type:"book",id:"9139",title:"Topics in Primary Care Medicine",subtitle:null,isOpenForSubmission:!1,hash:"ea774a4d4c1179da92a782e0ae9cde92",slug:"topics-in-primary-care-medicine",bookSignature:"Thomas F. Heston",coverURL:"https://cdn.intechopen.com/books/images_new/9139.jpg",editors:[{id:"217926",title:"Dr.",name:"Thomas F.",middleName:null,surname:"Heston",slug:"thomas-f.-heston",fullName:"Thomas F. Heston"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}}],latestBooks:[{type:"book",id:"7434",title:"Molecular Biotechnology",subtitle:null,isOpenForSubmission:!1,hash:"eceede809920e1ec7ecadd4691ede2ec",slug:"molecular-biotechnology",bookSignature:"Sergey Sedykh",coverURL:"https://cdn.intechopen.com/books/images_new/7434.jpg",editedByType:"Edited by",editors:[{id:"178316",title:"Ph.D.",name:"Sergey",middleName:null,surname:"Sedykh",slug:"sergey-sedykh",fullName:"Sergey Sedykh"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8545",title:"Animal Reproduction in Veterinary Medicine",subtitle:null,isOpenForSubmission:!1,hash:"13aaddf5fdbbc78387e77a7da2388bf6",slug:"animal-reproduction-in-veterinary-medicine",bookSignature:"Faruk Aral, Rita Payan-Carreira and Miguel Quaresma",coverURL:"https://cdn.intechopen.com/books/images_new/8545.jpg",editedByType:"Edited by",editors:[{id:"25600",title:"Prof.",name:"Faruk",middleName:null,surname:"Aral",slug:"faruk-aral",fullName:"Faruk Aral"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9569",title:"Methods in Molecular Medicine",subtitle:null,isOpenForSubmission:!1,hash:"691d3f3c4ac25a8093414e9b270d2843",slug:"methods-in-molecular-medicine",bookSignature:"Yusuf Tutar",coverURL:"https://cdn.intechopen.com/books/images_new/9569.jpg",editedByType:"Edited by",editors:[{id:"158492",title:"Prof.",name:"Yusuf",middleName:null,surname:"Tutar",slug:"yusuf-tutar",fullName:"Yusuf Tutar"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9839",title:"Outdoor Recreation",subtitle:"Physiological and Psychological Effects on Health",isOpenForSubmission:!1,hash:"5f5a0d64267e32567daffa5b0c6a6972",slug:"outdoor-recreation-physiological-and-psychological-effects-on-health",bookSignature:"Hilde G. Nielsen",coverURL:"https://cdn.intechopen.com/books/images_new/9839.jpg",editedByType:"Edited by",editors:[{id:"158692",title:"Ph.D.",name:"Hilde G.",middleName:null,surname:"Nielsen",slug:"hilde-g.-nielsen",fullName:"Hilde G. Nielsen"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"7802",title:"Modern Slavery and Human Trafficking",subtitle:null,isOpenForSubmission:!1,hash:"587a0b7fb765f31cc98de33c6c07c2e0",slug:"modern-slavery-and-human-trafficking",bookSignature:"Jane Reeves",coverURL:"https://cdn.intechopen.com/books/images_new/7802.jpg",editedByType:"Edited by",editors:[{id:"211328",title:"Prof.",name:"Jane",middleName:null,surname:"Reeves",slug:"jane-reeves",fullName:"Jane Reeves"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8063",title:"Food Security in Africa",subtitle:null,isOpenForSubmission:!1,hash:"8cbf3d662b104d19db2efc9d59249efc",slug:"food-security-in-africa",bookSignature:"Barakat Mahmoud",coverURL:"https://cdn.intechopen.com/books/images_new/8063.jpg",editedByType:"Edited by",editors:[{id:"92016",title:"Dr.",name:"Barakat",middleName:null,surname:"Mahmoud",slug:"barakat-mahmoud",fullName:"Barakat Mahmoud"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10118",title:"Plant Stress Physiology",subtitle:null,isOpenForSubmission:!1,hash:"c68b09d2d2634fc719ae3b9a64a27839",slug:"plant-stress-physiology",bookSignature:"Akbar Hossain",coverURL:"https://cdn.intechopen.com/books/images_new/10118.jpg",editedByType:"Edited by",editors:[{id:"280755",title:"Dr.",name:"Akbar",middleName:null,surname:"Hossain",slug:"akbar-hossain",fullName:"Akbar Hossain"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9157",title:"Neurodegenerative Diseases",subtitle:"Molecular Mechanisms and Current Therapeutic Approaches",isOpenForSubmission:!1,hash:"bc8be577966ef88735677d7e1e92ed28",slug:"neurodegenerative-diseases-molecular-mechanisms-and-current-therapeutic-approaches",bookSignature:"Nagehan Ersoy Tunalı",coverURL:"https://cdn.intechopen.com/books/images_new/9157.jpg",editedByType:"Edited by",editors:[{id:"82778",title:"Ph.D.",name:"Nagehan",middleName:null,surname:"Ersoy Tunalı",slug:"nagehan-ersoy-tunali",fullName:"Nagehan Ersoy Tunalı"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"9961",title:"Data Mining",subtitle:"Methods, Applications and Systems",isOpenForSubmission:!1,hash:"ed79fb6364f2caf464079f94a0387146",slug:"data-mining-methods-applications-and-systems",bookSignature:"Derya Birant",coverURL:"https://cdn.intechopen.com/books/images_new/9961.jpg",editedByType:"Edited by",editors:[{id:"15609",title:"Dr.",name:"Derya",middleName:null,surname:"Birant",slug:"derya-birant",fullName:"Derya Birant"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8686",title:"Direct Torque Control Strategies of Electrical Machines",subtitle:null,isOpenForSubmission:!1,hash:"b6ad22b14db2b8450228545d3d4f6b1a",slug:"direct-torque-control-strategies-of-electrical-machines",bookSignature:"Fatma Ben Salem",coverURL:"https://cdn.intechopen.com/books/images_new/8686.jpg",editedByType:"Edited by",editors:[{id:"295623",title:"Associate Prof.",name:"Fatma",middleName:null,surname:"Ben Salem",slug:"fatma-ben-salem",fullName:"Fatma Ben Salem"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},subject:{topic:{id:"230",title:"Quantum Mechanics",slug:"quantum-mechanics",parent:{title:"Physics",slug:"physics"},numberOfBooks:3,numberOfAuthorsAndEditors:81,numberOfWosCitations:75,numberOfCrossrefCitations:33,numberOfDimensionsCitations:68,videoUrl:null,fallbackUrl:null,description:null},booksByTopicFilter:{topicSlug:"quantum-mechanics",sort:"-publishedDate",limit:12,offset:0},booksByTopicCollection:[{type:"book",id:"10076",title:"Quantum Mechanics",subtitle:null,isOpenForSubmission:!1,hash:"78f2b316d6bb97464dbbf9b683164aff",slug:"quantum-mechanics",bookSignature:"Paul Bracken",coverURL:"https://cdn.intechopen.com/books/images_new/10076.jpg",editedByType:"Edited by",editors:[{id:"92883",title:"Prof.",name:"Paul",middleName:null,surname:"Bracken",slug:"paul-bracken",fullName:"Paul Bracken"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"7396",title:"Panorama of Contemporary Quantum Mechanics",subtitle:"Concepts and Applications",isOpenForSubmission:!1,hash:"e78f2cfea2dec9fab1f269c994faa0d4",slug:"panorama-of-contemporary-quantum-mechanics-concepts-and-applications",bookSignature:"Tuong T. Truong",coverURL:"https://cdn.intechopen.com/books/images_new/7396.jpg",editedByType:"Edited by",editors:[{id:"143434",title:"Prof.",name:"Trong Tuong",middleName:null,surname:"Truong",slug:"trong-tuong-truong",fullName:"Trong Tuong Truong"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"52",title:"Wave Propagation",subtitle:null,isOpenForSubmission:!1,hash:null,slug:"wave-propagation",bookSignature:"Andrey Petrin",coverURL:"https://cdn.intechopen.com/books/images_new/52.jpg",editedByType:"Edited by",editors:[{id:"7760",title:"Dr.",name:"Andrey",middleName:"Borisovich",surname:"Petrin",slug:"andrey-petrin",fullName:"Andrey Petrin"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],booksByTopicTotal:3,mostCitedChapters:[{id:"14154",doi:"10.5772/14459",title:"Microwave Sensor Using Metamaterials",slug:"microwave-sensor-using-metamaterials",totalDownloads:3777,totalCrossrefCites:19,totalDimensionsCites:32,book:{slug:"wave-propagation",title:"Wave Propagation",fullTitle:"Wave Propagation"},signatures:"Ming Huang and Jingjing Yang",authors:[{id:"17613",title:"Dr.",name:"Ming",middleName:null,surname:"Huang",slug:"ming-huang",fullName:"Ming Huang"},{id:"18836",title:"Dr.",name:"Jingjing",middleName:null,surname:"Yang",slug:"jingjing-yang",fullName:"Jingjing Yang"}]},{id:"14165",doi:"10.5772/14001",title:"On the Electrodinamics of Space-Time Periodic Mediums in a Waveguide of Arbitrary Cross Section",slug:"on-the-electrodinamics-of-space-time-periodic-mediums-in-a-waveguide-of-arbitrary-cross-section",totalDownloads:1398,totalCrossrefCites:0,totalDimensionsCites:6,book:{slug:"wave-propagation",title:"Wave Propagation",fullTitle:"Wave Propagation"},signatures:"Eduard A. Gevorkyan",authors:[{id:"15523",title:"Prof.",name:"Eduard A.",middleName:null,surname:"Gevorkyan",slug:"eduard-a.-gevorkyan",fullName:"Eduard A. Gevorkyan"}]},{id:"14175",doi:"10.5772/13868",title:"Electromagnetic Waves Generated by Line Current Pulses",slug:"electromagnetic-waves-generated-by-line-current-pulses",totalDownloads:1556,totalCrossrefCites:0,totalDimensionsCites:5,book:{slug:"wave-propagation",title:"Wave Propagation",fullTitle:"Wave Propagation"},signatures:"Andrei B. Utkin",authors:[{id:"16132",title:"Dr.",name:"Andrei",middleName:"B.",surname:"Utkin",slug:"andrei-utkin",fullName:"Andrei Utkin"}]}],mostDownloadedChaptersLast30Days:[{id:"71370",title:"Complex Space Nature of the Quantum World: Return Causality to Quantum Mechanics",slug:"complex-space-nature-of-the-quantum-world-return-causality-to-quantum-mechanics",totalDownloads:214,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"quantum-mechanics",title:"Quantum Mechanics",fullTitle:"Quantum Mechanics"},signatures:"Ciann-Dong Yang and Shiang-Yi Han",authors:[{id:"158670",title:"Prof.",name:"Ciann-Dong",middleName:null,surname:"Yang",slug:"ciann-dong-yang",fullName:"Ciann-Dong Yang"},{id:"315900",title:"Dr.",name:"Shiang-Yi",middleName:null,surname:"Han",slug:"shiang-yi-han",fullName:"Shiang-Yi Han"}]},{id:"73016",title:"Exactly Solvable Problems in Quantum Mechanics",slug:"exactly-solvable-problems-in-quantum-mechanics",totalDownloads:233,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"quantum-mechanics",title:"Quantum Mechanics",fullTitle:"Quantum Mechanics"},signatures:"Lourdhu Bruno Chandrasekar, Kanagasabapathi Gnanasekar and Marimuthu Karunakaran",authors:[{id:"239576",title:"Dr.",name:"Marimuthu",middleName:null,surname:"Karunakaran",slug:"marimuthu-karunakaran",fullName:"Marimuthu Karunakaran"},{id:"252354",title:"Dr.",name:"Bruno Chandrasekar",middleName:null,surname:"L",slug:"bruno-chandrasekar-l",fullName:"Bruno Chandrasekar L"},{id:"325784",title:"Dr.",name:"K",middleName:null,surname:"Gnanasekar",slug:"k-gnanasekar",fullName:"K Gnanasekar"}]},{id:"71814",title:"Entropy in Quantum Mechanics and Applications to Nonequilibrium Thermodynamics",slug:"entropy-in-quantum-mechanics-and-applications-to-nonequilibrium-thermodynamics",totalDownloads:210,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"quantum-mechanics",title:"Quantum Mechanics",fullTitle:"Quantum Mechanics"},signatures:"Paul Bracken",authors:[{id:"92883",title:"Prof.",name:"Paul",middleName:null,surname:"Bracken",slug:"paul-bracken",fullName:"Paul Bracken"}]},{id:"14154",title:"Microwave Sensor Using Metamaterials",slug:"microwave-sensor-using-metamaterials",totalDownloads:3777,totalCrossrefCites:19,totalDimensionsCites:32,book:{slug:"wave-propagation",title:"Wave Propagation",fullTitle:"Wave Propagation"},signatures:"Ming Huang and Jingjing Yang",authors:[{id:"17613",title:"Dr.",name:"Ming",middleName:null,surname:"Huang",slug:"ming-huang",fullName:"Ming Huang"},{id:"18836",title:"Dr.",name:"Jingjing",middleName:null,surname:"Yang",slug:"jingjing-yang",fullName:"Jingjing Yang"}]},{id:"71547",title:"Dipolar Interactions: Hyperfine Structure Interaction and Fine Structure Interactions",slug:"dipolar-interactions-hyperfine-structure-interaction-and-fine-structure-interactions",totalDownloads:168,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"quantum-mechanics",title:"Quantum Mechanics",fullTitle:"Quantum Mechanics"},signatures:"Betül Çalişkan and Ali Cengiz Çalişkan",authors:[{id:"199110",title:"Dr.",name:"Betül",middleName:null,surname:"Çalişkan",slug:"betul-caliskan",fullName:"Betül Çalişkan"},{id:"208732",title:"Dr.",name:"Ali Cengiz",middleName:null,surname:"Çalişkan",slug:"ali-cengiz-caliskan",fullName:"Ali Cengiz Çalişkan"}]},{id:"73269",title:"Equations of Relativistic and Quantum Mechanics (without Spin)",slug:"equations-of-relativistic-and-quantum-mechanics-without-spin-",totalDownloads:121,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"quantum-mechanics",title:"Quantum Mechanics",fullTitle:"Quantum Mechanics"},signatures:"Vahram Mekhitarian",authors:[{id:"315832",title:"Dr.",name:"Vahram",middleName:null,surname:"Mekhitarian",slug:"vahram-mekhitarian",fullName:"Vahram Mekhitarian"}]},{id:"71964",title:"Uncertainty Relations",slug:"uncertainty-relations",totalDownloads:129,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"quantum-mechanics",title:"Quantum Mechanics",fullTitle:"Quantum Mechanics"},signatures:"Kenjiro Yanagi",authors:[{id:"315022",title:"Prof.",name:"Kenjiro",middleName:null,surname:"Yanagi",slug:"kenjiro-yanagi",fullName:"Kenjiro Yanagi"}]},{id:"72922",title:"Analysis of Quantum Confinement and Carrier Transport of Nano-Transistor in Quantum Mechanics",slug:"analysis-of-quantum-confinement-and-carrier-transport-of-nano-transistor-in-quantum-mechanics",totalDownloads:118,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"quantum-mechanics",title:"Quantum Mechanics",fullTitle:"Quantum Mechanics"},signatures:"Aynul Islam and Anika Tasnim Aynul",authors:[{id:"316001",title:"Dr.",name:"Islam",middleName:null,surname:"Aynul",slug:"islam-aynul",fullName:"Islam Aynul"},{id:"325161",title:"BSc.",name:"Anika Tasnim",middleName:null,surname:"Aynul",slug:"anika-tasnim-aynul",fullName:"Anika Tasnim Aynul"}]},{id:"71655",title:"Transitions between Stationary States and the Measurement Problem",slug:"transitions-between-stationary-states-and-the-measurement-problem",totalDownloads:126,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"quantum-mechanics",title:"Quantum Mechanics",fullTitle:"Quantum Mechanics"},signatures:"María Esther Burgos",authors:[{id:"96880",title:"Prof.",name:"Maria Esther",middleName:null,surname:"Burgos",slug:"maria-esther-burgos",fullName:"Maria Esther Burgos"}]},{id:"73158",title:"Nature of Temporal (t > 0) Quantum Theory: Part II",slug:"nature-of-temporal-t-0-quantum-theory-part-ii",totalDownloads:119,totalCrossrefCites:0,totalDimensionsCites:0,book:{slug:"quantum-mechanics",title:"Quantum Mechanics",fullTitle:"Quantum Mechanics"},signatures:"Francis T.S. Yu",authors:[{id:"300154",title:"Emeritus Prof.",name:"Francis",middleName:null,surname:"Yu",slug:"francis-yu",fullName:"Francis Yu"}]}],onlineFirstChaptersFilter:{topicSlug:"quantum-mechanics",limit:3,offset:0},onlineFirstChaptersCollection:[],onlineFirstChaptersTotal:0},preDownload:{success:null,errors:{}},aboutIntechopen:{},privacyPolicy:{},peerReviewing:{},howOpenAccessPublishingWithIntechopenWorks:{},sponsorshipBooks:{sponsorshipBooks:[{type:"book",id:"10176",title:"Microgrids and Local Energy Systems",subtitle:null,isOpenForSubmission:!0,hash:"c32b4a5351a88f263074b0d0ca813a9c",slug:null,bookSignature:"Prof. Nick Jenkins",coverURL:"https://cdn.intechopen.com/books/images_new/10176.jpg",editedByType:null,editors:[{id:"55219",title:"Prof.",name:"Nick",middleName:null,surname:"Jenkins",slug:"nick-jenkins",fullName:"Nick Jenkins"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter"}}],offset:8,limit:8,total:1},route:{name:"profile.detail",path:"/profiles/132320/tetsuji-yamaoka",hash:"",query:{},params:{id:"132320",slug:"tetsuji-yamaoka"},fullPath:"/profiles/132320/tetsuji-yamaoka",meta:{},from:{name:null,path:"/",hash:"",query:{},params:{},fullPath:"/",meta:{}}}},function(){var t;(t=document.currentScript||document.scripts[document.scripts.length-1]).parentNode.removeChild(t)}()