Proceedings HM 2014

FACULTY OF MECHANICAL AND CIVIL ENGINEERING KRALJEVO UNIVERSITY OF KRAGUJEVAC

KRALJEVO SERBIA

THE EIGHTH INTERNATIONAL TRIENNIAL CONFERENCE

HEAVY MACHINERY HM 2014

PROCEEDINGS

Zlatibor, June 25 June 28 2014.


KRALJEVO SERBIA

THE EIGHTH INTERNATIONAL TRIENNIAL CONFERENCE

HEAVY MACHINERY HM 2014

PROCEEDINGS

ORGANIZATION SUPPORTED BY:

Ministry of Education and Science, Republic of Serbia

Zlatibor, June 25 June 28 2014


KRALJEVO SERBIA

PUBLISHER: Faculty of Mechanical and Civil Engineering, Kraljevo EDITORS: Prof. dr Milomir Gai, mech. eng. PRINTOUT: SaTCIP d.o.o. Vrnjacka Banja TECHNICAL COMMITTEE Dr Vladimir Stojanovi Milan Bii Zoran Bogievi Goran Bokovi Marina Bokovi Vladan Grkovi Marko Nikoli Aleksandra Petrovi Nenad Stoji Miljan Veljovi Aleksandar Vrani Vladimir orevi Bojan Beloica Slobodan Bukarica Milorad Stamboli No. of copies: 200 REVIEWS: All papers have been reviewed by members of scientific committee


KRALJEVO SERBIA

CONFERENCE CHAIRMAN Prof. dr Milomir Gai, FMCE Kraljevo INTERNATIONAL SCIENTIFIC PROGRAM COMMITTEE CHAIRMAN Prof. Dr Mile Savkovi, FMCE Kraljevo VICE-CHAIRMAN Prof. Dr Milan Kolarevi, FMCE Kraljevo, Serbia MEMBERS 1. Prof. Dr M. Alamoreanu, TU Bucharest,

Romania 2. Prof. Dr S. Arsovski, FME Kragujevac,

Serbia 3. Prof. Dr D. Atmadzhova, VTU Todor

Kableshkov, Sofia, Bulgaria 4. Prof. Dr M. Berg, Royal Institut of

Tecnology-KTH, Sweden 5. Prof. Dr H. Bogdevicius, Technical

University, Vilnus, Lithuania 6. Prof. Dr S. Bonjak, FME Belgrade, Serbia 7. Prof. Dr A. Bruja, TU Bucharest, Romanija 8. Prof. Dr Z. Buevac, FME Belgrade, Serbia 9. Prof. Dr R.Bulatovi, FMCE Kraljevo,

Serbia 10. Prof. Dr A. Bukvi, FME East Sarajevo,

Bosnia and Herzegovina 11. Prof. Dr M. Dedi, FMCE Kraljevo, Serbia 12. Prof. Dr A. I. Dotsenko, MGSU, Moscow,

Russia 13. Prof. Dr R. Durkovi, FME Podgorica,

Montenegro 14. Prof. Dr M. api, FMCE Kraljevo, Serbia 15. Prof. Dr Z. inovi, Integrated

MicroSystem, Vienna, Austria 16. Prof. Dr K. Ehmann, Northwestern

University, Chicago, USA 17. Prof. Dr A. Emeljanova, HGTUSA Harkov,

Ukraine 18. Prof. Dr V. Filipovi, FMCE Kraljevo,

Serbia 19. Prof. Dr C. Fragassa, University of

Bologna, Italy

20. Prof. Dr M. Gagl, Integrated MicroSystem, Vienna, Austria

21. Prof. Dr D. Golubovi, FME East Sarajevo, Bosnia and Herzegovina

22. Prof. Dr V. Jovievi, FME Banja Luka, Bosnia and Herzegovina

23. Prof. Dr B. Jerman, FME Ljubljana, Slovenia

24. Prof. Dr Z. Jugovi, Tehnical Faculty aak, Serbia

25. Prof. Dr V. Karamarkovi, FMCE Kraljevo, Serbia

26. Prof. Dr M. Karasahin, Demirel Univerity, Istanbul, Turkey

27. Prof. Dr I. Kirienko, HNADU Kiev, Ukraine

28. Prof. Dr K. Kocman, Tecnical University of Brno, Czech Republic

29. Prof. Dr S. Kolakovi, Faculty of Tehnical Sciences, Novi Sad, Serbia

30. Prof. Dr M. Kostic, Northern Illinois University, DeKalb, USA

31. Prof. Dr M. Krlik, FME Bratislava, Slovakia

32. Prof. Dr E. Kudrjavcev, MGSU, Moskow, Russia

33. Prof. Dr . Lainovi, Faculty of Tehnical Sciences, Novi Sad, Serbia

34. Prof. Dr LJ. Luki, FMCE Kraljevo, Serbia 35. Prof. Dr Z. Marinkovi, FME Ni, Serbia 36. Prof. Dr N. Meerin, MGSU, Moskow,

Russia 37. Prof. Dr I. I. Nazarenko, KNUBA Kiev,

Ukraine


KRALJEVO SERBIA

38. Prof. Dr N. Nedi, FMCE Kraljevo, Serbia 39. Prof. Dr N. Nenov, VTU Todor

Kableshkov, Sofia, Bulgaria 40. Prof. Dr V. Nikoli, FME Ni, Serbia 41. Prof. Dr E. Nikolov, Technical University,

Sofia, Bulgaria 42. Prof. Dr M. Ognjanovi, FME Belgrade,

Serbia 43. Prof. Dr J. Peterka, FMS&T, Trnava,

Slovakia 44. Prof. Dr D. Petrovi, FMCE Kraljevo,

Serbia 45. Prof. Dr Z. Petrovi, FMCE Kraljevo,

Serbia 46. Prof. Dr J. Polajnar, BC University, Prince

George, Canada 47. Prof. Dr V. Radonjanin, Faculty of Tehnical

Sciences, Novi Sad, Serbia 48. Prof. Dr V. Raievi, FME Kosovska

Mitrovica, Serbia

49. Prof. Dr M. Rajovi, FMCE Kraljevo, Serbia

50. Prof. Dr M. Stefanov, FME Kragujevac, Serbia

51. Prof. Dr D. Sever, Maribor, Civil Engineering, Slovenia

52. Prof. Dr M. A. Stepanov, MGSU, Moskow, Russia

53. Prof. Dr I. S. Surovcev, VGSU, Voronezh, Russia

54. Prof. Dr Z. oki, FMCE Kraljevo, Serbia 55. Prof. Dr LJ. Tanovi, FME Belgrade, Serbia 56. Prof. Dr S. Trifunovi, FMCE Kraljevo,

Serbia 57. Prof. Dr J. Vladi, Faculty of Tehnical

Sciences, Novi Sad, Serbia 58. Prof. Dr M. Vukievi, FMCE Kraljevo,

Serbia 59. Prof. Dr K. Weinert, University of

Dortmund, Germany 60. Prof. Dr N. Zrni, FME Belgrade, Serbia

ORGANIZING COMMITTEE CHAIRMAN: Prof. Dr Ljubomir Luki, FMCE Kraljevo VICE-CHAIRMAN: Prof. Dr Zlatan oki, FMCE Kraljevo, Serbia MEMBERS: Doc. Dr S. iri-Kosti, FMCE Kraljevo, Serbia Doc. Dr Lj. Dubonji, FMCE Kraljevo, Serbia Doc. Dr O. Eri, FMCE Kraljevo, Serbia Doc. Dr R. Karamarkovi, FMCE Kraljevo, Serbia Doc. Dr M. Maraevi, FMCE Kraljevo, Serbia Doc. Dr D. Pri, FMCE Kraljevo, Serbia Doc. Dr S. alini, FMCE Kraljevo, Serbia

M.Sc. M. Bjeli, FMCE Kraljevo, Serbia M.Sc. N. Bogojevi, FMCE Kraljevo, Serbia M.Sc. Z. Glavi, FMCE Kraljevo, Serbia M.Sc. Lj. Lalovi, FMCE Kraljevo, Serbia M.Sc. G. Markovi, FMCE Kraljevo, Serbia M.A. N. Pavlovi, FMCE Kraljevo, Serbia M.Sc. B. Radievi, FMCE Kraljevo, Serbia M.Sc. N. Zdravkovi, FMCE Kraljevo, Serbia


KRALJEVO SERBIA

PREFACE The Faculty of Mechanical Engineering Kraljevo has been traditionally organizing the international scientific conference devoted to heavy machinery every three years. The VIII International Scientific Conference HM 2014 is considering modern methods and new technologies in the fields of transport design in machinery, control energy, production technologies, urban engineering and civili engineering through thematic sessions for the purpose of sustainable competitiveness of economic systems. Modern technologies are exposed to fast changes at the global world level so that their timely application both in large industrial systems and in medium and small enterprises is of considerable importance for the entire development and technological progress of economy as a whole. The VIII International Scientific Conference Heavy Machinery HM 2014 is a place for exchange of experiences and results accomplished in domestic and foreign science and practice, with the goal to indicate directions of further development of our industry on its way toward integration in european and world economic trends. Exchange of experiences between our and foreign scientific workers should contribute to extension of international scientific-technical collaboration, initiation of new international scientific-research projects and broader international collaboration among universities. The papers which will be presented at this Conference have been classified into seven thematic fields:

A. EARTH-MOVING AND TRANSPORTATION MACHINERY B. PRODUCTION TECHNOLOGIES C. CIVIL ENGINEERING AND MATERIALS D. AUTOMATIC CONTROL, ROBOTICS AND FLUID TECHNIQUE E. MACHINE DESIGN AND MECHANICS F. RAILWAY ENGINEERING G. URBAN ENGINEERING, THERMAL TECHNIQUE AND ENVIRONMENT

PROTECTION Within this Conference, the First International Students Symposium will be held. The aim is to open a scientific discussion on this actual problem in industry among young students. The sponsorship by the Ministry of Science of the Republic of Serbia is the proper way to promote science and technology in the area of mechanical engineering in Serbia. On behalf of the organizer, I would like to express our thanks to all organizations and institutions that have supported this Conference. I would also like to extend our thanks to all authors and participants from abroad and from our country for their contribution to the Conference. And last but not the least, dear guests and participants in the Conference, I wish you a good time in Kraljevo Vrnjaka Banja and see you again at the Eight Conference, in three years. Kraljevo Zlatibor, June 2014 Conference Chairman, Prof. Dr Milomir Gai, mech eng.

PLENARY SESSION MODELLING AND WORKING SIMULATION OF THE MECHANISM OF AXIAL PISTON 1-8 HYDROSTATIC PUMPS USING DENAVIT-HARTENBERG METHOD Adrian Bruja, Marian Dima

DEFINITION RATIONAL GATE FRAME SIZE DISTRIBUTION UNIT DOUBLE PISTON CONCRETE 9-13 PUMP WITH HYDRAULIC DRIVE Inga A. Emeliyanova, . A. Zadorozhny, D. V. Legeyda, N. A. Melencov

MECHANICAL BEHAVIOUR AND FRICTION EVOLUTION ON BOLTED CONNECTIONS 15-23 Dario Croccolo

DYNAMIC ANALYSIS OF MECHANICAL SYSTEMS 25-30 Evgeniy Kudryavtev, A. A. Ruchkin

SESSION A: EARTH-MOVING AND TRANSPORTATION MACHINERY GENERAL CLASSIFICATION OF SMALL-SIZED TECHNOLOGICAL SETS FOR PRODUCTION 1-4 OF DRY BUILDING MIXTURES Inga Emelyanova, Vladimir Blazhko

POST-EJECTION FAILURE MODE OF POST DRIVING MACHINES 5-11 William Singhose, Dooroo Kim, Joshua Vaughan

DETERMINING THE INVERSE KINEMATICS MODEL OF A BUCKET EXCAVATORS DIGGING 13-16 EQUIPMENT Marian Dima, Ctlin Frncu, Radu Ghelmeci

ADAPTATION OF EARTH-MOVING MAHINES TO EXTERNAL LOADING CONDITIONS 17-21 Valery Shevchenko

INCREASING THE EFFICIENCY OF THE OPERATION OF THE BATCH-TYPE EARTH-MOVING 23-28 MACHINES AT THE EXPENSE OF USING THE PNEUMATIC STORAGE SYSTEM Leonid Khmara, Anton Kholodov

FRACTURE ANALYSIS OF THE HYDRAULIC TRUCK CRANE ATLAS 3006 29-35 Mile Savkovi, Milomir Gai, Neboja Zdravkovi, Goran Bokovi, Goran Pavlovi

APPLICATION OF THE NUMERICAL METHODS FOR DYNAMIC ANALYSIS OF 37-42 TRANSPORTSYSTEMS WITH ROPE Jovan Vladi, Dragan ivani, Igor Dini, Radomir oki, Anto Gaji

THE DEVELOPMENT OF HYDROSTATIC DRIVE TRANSMISSIONS OF WHEEL LOADERS 43-48 Jovan Pavlovi, Dragoslav Janoevi, Vesna Jovanovi, Sa Petrovi

ABOUT CHOOSING THE RIGHT COMPUTATIONAL MODEL FOR FEA STRESS ANALYSIS 49-57 OF DRILLING RIGS AND WELL SERVICING STRUCTURES IN OIL INDUSTRY Radoslav Simi, Nikola Brklja

ROAD-HOLDING ABILITY OF THE MOTOR GRADER IN THE PROCESS OF PERFORMING WORK 59-67 OPERATIONS Valery Shevchenko, Olexandra Chaplygina, Zhanna Beztsennaya

5D MODELLING OF MECHANICAL SYSTEMS 69-71 Evgeniy Kudryavtev

NEW EFFECTIVE MACHINE FOR ROLLING HOLES DURING INSTALLING UNDERGROUND 73-74 COMMUNICATIONS IN URBAN CONSTRUCTION Anatoly Dotsenko

KINEMATICS COMPUTATIONAL MODELLING OF SELF-ERECTING TOWER CRANES ERECTION 75-84 MECHANISM Ctlin Frncu, Marian Dima

RESEARCH AND THE CREATION OF ENERGY-EFFICIENT VIBRATION MACHINES BASED 85-89 ON THE STRESS-STRAIN STATE OF METAL AND TECHNOLOGICAL ENVIRONMENTS Ivan Ivanovich Nazarenko, Anatoliy Tofiliyovych Sviderskyy, Mykola Mykolayovych

TOP TIER TECHNOLOGY IN SUBWAY TUNNELLING USING A MECHATRONIC DRIVING SHIELD 91-97 Ioan Brdescu, Amelitta Legendi

FREE VIBRATIONS OF THE PLANAR GANTRY-LIKE STRUCTURES 99-104 Vlada Gai, Aleksandar Obradovi, Nenad Zrni

OPTIMIZATION OF THE BOX SECTION OF THE MAIN GIRDERS OF THE BRIDGE CRANE 105-112 FOR THE CASE OF PLACING THE RAIL IN THE MIDDLE OF THE TOP FLANGE Goran Pavlovic, Milomir Gasic, Mile Savkovic, Radovan Bulatovic, Nebojsa Zdravkovic

OPTIMAL SYNTHESIS OF THE DRIVING MECHANISM OF BASKET ARTICULATED TRUCKS 113-118 Dragoslav Janoevi, Jovan Pavlovi, Vesna Jovanovi, Predrag Mili

NUMERICAL ANALYSIS OF ELEVATOR ROPES VIBRATION WITH TIME VARYING LENGTH 119-124 Jovan Vladi, Radomir oki, Anto Gaji, Dragan ivani

THE INFLUENCE OF STRUCTURE ANCHORING ON EIGENVALUES AND TRANSLATIONS 125-130 Goran Radoii, Miomir Jovanovi, Ivan Savi

THEORETICAL ASPECTS OF ZIP LINE ANALYSIS 131-136 Mircea Alamoreanu, Andrei Vasilescu

TIP-OVER STABILITY OF CRAWLER CRANES WITH MOVABLE COUNTERWEIGHT 137-143 Huasen Liu, William Singhose, Wenming Cheng

KINEMATICS OF THE TRUCK MOUNTED HYDRAULIC CRANES 145-150 Boris Jerman, Jurij Hladnik, Vlada Gai, Milo orevi

DETERMINING THE FORWARD KINEMATICS MODEL OF A BUCKET EXCAVATORS 151-155 DIGGING EQUIPMENT Marian Dima, Ctlin Frncu, Radu Ghelmeci

CASE STUDY OF PRODUCT INNOVATION BASED ON SPECIAL CRANE TROLLEY 157-164 Zoran Petrovi, Ugljea Bugari, Duan Petrovi

SIMPLIFIED LIFE CYCLE ASSESSMENT OF A CONVEYOR BELTING 165-170 Milos Djordjevic, Nenad Zrnic, Boris Jerman

SELECTION OF THE BASIC PARAMETERS OF GENERAL PURPOSE TELESCOPIC BELT 171-175 CONVEYOR Rodoljub Vujanac, Nenad Miloradovic

DESIGN-IN FAULTS - THE REASON FOR SERIOUS DRAWBACKS IN HIGH CAPACITY 177-182 BUCKET WHEEL EXCAVATOR EXPLOITATION Nebojsa Gnjatovic, Goran Milojevic, Ivan Milenovic, Aleksandar Stefanovic

THE EQUATIONS OF MOTION OF THE CRANE WITH LOADING-UNLOADING TROLLEY 183-186 ON THE SLEWING PLATFORM Spasoje Trifkovic, Milomir Gasic, Nebojsa Radic, Miroslav Milutinovic

THE KINEMATIC AND DYNAMIC ANALYSIS OF THE HYDRAULIC EXCAVATORS 187-192 Vesna Jovanovi, Dragoslav Janoevi, Jovan Pavlovi

SESSION B: PRODUCTION TECHNOLOGIES IDENTIFICATION OF SUPPORTING ELEMENTS DYNAMICS OF PRODUCTION MACHINES USING 1-6 DYNAMICS OF RIGID BODIES SYSTEM Radomir Slavkovi, Ivan Milievi, Nedeljko Dui, Marko Popovi, Zvonimir Jugovi

NEW CONCEPT OF MULTI-AGENT CAPP SYSTEM IN INTELIGENT MANUFACTURING SYSTEMS 7-12 Ljubomir Lukic, Mirko Djapic, Aleksandra Petrovic, Veda Kilibarda

THE USE OF BIOLOGICALLY-INSPIRED ALGORITHMS FOR THE OPTIMIZATION OF MACHINING 13-18 PARAMETERS Goran Miodragovi, Radovan Bulatovi, Slobodan Ivanovi, Marina Bokovi

MACHINING PARAMETERS INFLUENCE ON CUTTING FORCE USED FOR TOOL PATH 19-25 OPTIMIZATION IN END MILLING Aleksandra Petrovi, Ljubomir Luki, Marina Pljaki

MARKETING ORIENTED ORGANIZATIONAL CULTURE AS PREREQUISITE FOR TQM 27-35 IMPLEMENTATION: THE CASE STUDY OF SERBIAN MECHANICAL INDUSTRY Ljiljana Peci, Milan Kolarevi

RECOGNIZING MAG PROCESS PARAMETERS ON THE BASIS OF THE SOUND EMITTED 37-42 Marina Pljaki, Miomir Vukievi, Milan Kolarevi, Mio Bjeli

APPLICATION OF SUBMATRICES FOR SOLVING PHASE PROCESSES BY THE LINEAR 43-48 PROGRAMMING METHOD Milan Kolarevi, Vladan Grkovi, Zvonko Petrovi, Miloje Rajovi

APPLICATION OF THE COPRAS METHOD FOR SELECTION OF COMPETI8/21/2014TIVE 49-54 NON-CONVENTIONAL MACHINING PROCESSES Milo Madi, Miroslav Radovanovi, Danijel Markovi, Goran Petrovi

EVALUATION OF QUALITY AND EFFICIENCY OF TECHNOLOGIES FOR MAKING 55-61 AXI-SYMMETRICAL PROFILES METHOD OF SUPERIORITY AND INFERIORITY Dragana Temeljkovski, Dragan Temeljkovski

ON THE EFFECT OF NORMAL LOAD AND SLIDING SPEED ON WEAR UNDER DRY SLIDING 63-68 CONTACT ON THE BRASS (70-30, 60-40) Dragan Milcic, Amir M. Rashid, Boban Anelkovi, Mustafa A. Mustafa

IMPLEMENTATION OF THE RCM METHODOLOGY ON THE EXAMPLE OF CITY WATERWORKS 69-78 Zoran Petrovic, Zlatan Car, Branko Radicevic, Leon ikule, Vladan Grkovic

MODELING AND NUMERICAL ANALYSIS OF WIRE TEMPERATURE IN GMA WELDING 79-82 Mio Bjeli, Karel Kovanda, Ladislav Kolak, Marie Kolakov, Petr Vondrou

COMPLEXITY IN PRODUCTION SYSTEMS 83-87 Elvis Hozdi, Emine Hozdi

SESSION C: CIVIL ENGINEERING AND MATERIALS DRAINAGE WELLS ON THE LANDSLIDE - SLOBODA BRIDGE IN NOVI SAD 1-7 Milinko Vasi, Mitar ogo, Branko Jelisavac

MICROSTRUCTURAL ANALYSIS OF CONSTRUCTIONAL MATERIALS 9-15 Milena Rangelov, Vlastimir Radonjanin, Mirjana Maleev, Jovana Kalianin

ESTIMATION OF MARSHALL STABILITY OF STEEL FIBER REINFORCED ASPHALT CONCRETE 17-20 ADAPTIVE USING NEURO-FUZZY INFERENCE SYSTEM Nihat Morova, Sercan Serin, Serdal Terzi, Mehmet Saltan, Mustafa Karaahin

GEOTECHNICAL CONDITIONS FOR FOUNDATION OF COMPRESSOR IN VELEBIT 21-24 Mitar ogo, Milinko Vasi, Rada Stevanovi

KNOWLEDGE INNOVATION TRENDS ON A STANDARDIZATION PLATFORM - PARALLEL: CIVIL 25-33 ENGINEERING AND RAILWAY ENGINEERING ivadin Mici, Slobodan Petrovi

ALTERATION IN MECHANICAL PROPRIETIES OF PORCELAIN PASSING BY A BENDING 35-43 PROCESS Cristiano Fragassa, Ana Pavlovic, Pier Paolo Conti, Olivera Eric

SYSTEM FOR MONITORING THE WELDING OPERATION 45-49 Olivera Eric Cekic, Radomir Jovii, Branko Zrili, Neboja Panteli

INVESTIGATION OF STEEL PROPERTIES FOR SIDE FRAMES OF SCRAPER CONVEYOR PANS 51-54 Diana Glushkova, Ye. Voronova, Valentina Tarabanova, Larisa Rak

DEPENDENCE OF MECHANICAL PROPERTIES OF THE BASE METAL AND WELDED JOINT 55-59 OF THE HIGH STRENGTH STEEL S690QL ON ELEVATED TEMPERATURES Dusan Arsic, Vuki Lazi, Andreja Ili, Lozica Ivanovi, Srbislav Aleksandrovi, Milan orevi

SESSION D: AUTOMATIC CONTROL, ROBOTICS AND FLUID TECHNIQUE MODELLING, SIMULATION AND CASCADE NAVIGATION CONTROL OF A PROTOTYPE CARGO 1-6 VESSEL Erol Uyar, Semih Arkan, Mcahid Candan, Nail Akura

DEFINITION OF POWER AND KINEMATIC PARAMETERS OF FULL-FLOW HYDROSTATIC 7-10 TRANSMISSION Vladimir Alexeevich Zhulai, Vladimir Ivanovich Yenin, Evgenii Vladimirovich

THE LOCALIZATION OF THE ROBOTIC MOBILE PLATFORMS FOR CONSTRUCTIONS WITH 11-15 TRACKER LASER AND SMARTTRACK SENSOR Radu Ghelmeci, Marian Dima

COMPARISON OF TWO APPROACHES TO IDENTIFICATION PROCESS OF CONDENSER 17-22 IN THERMAL POWER PLANT Novak Nedi, Saa Prodanovi

HARMONIC ANALYSIS OF A PNEUMATIC FIXED ORIFICE 23-28 Dragan Pri, Ljubia Dubonji, Vladimir Stojanovi

MATHEMATICAL MODELING, IDENTIFICTION AND OPTIMIZATION OF PARAMETERS 29-34 OF THE VALVE PLATE OF THE WATER HYDRAULIC PISTON-AXIAL PUMP/MOTOR Radovan Petrovic, Nenad Todic, Miroslav Zivkovic, Zoran Glavi

COMPUTER CONTROL ON POSITIONING STEPPER DRIVE LABORATORY STAND 35-40 Vasil Dimitrov, Ivan Milenov, Emiliya Dimitrova

POSITION CONTROL OF A THREE DEGREE OF FREEDOM ROBOT 41-44 Gkmen Katipolu, Sava Takan

RECURSIVE ESTIMATION OF THE TAKAGI-SUGENO MODELS I: FUZZY CLUSTERING 45-50 AND THE PREMISE MEMBERSHIP FUNCTIONS ESTIMATION Vojislav Filipovic, Vladimir Djordjevic

ENERGY PERFORMANCE CONSTANT POWER MOTION CONTROL OF ROBOTIZED MINING 51-59 TRUCK Denis Pogosov

DESIGN THE DIGITAL INTERNAL MODEL CONTROL OF AN ELECTROMECHANICAL 61-66 POSITIONING SYSTEM WITH CONTROLLED JERK Mihaylo Stoychitch

DESIGN OF PID CONTROLLERS FOR HIGH ORDER SYSTEMS 67-72 Ljubisa Dubonjic, Novak Nedic, Dragan Prsic

ROBUST AKAIKES CRITERION FOR MODEL ORDER SELECTION 73-78 Vladimir Stojanovic, Vojislav Filipovic

SIMULATION RESULTS OF PARAMETER ESTIMATION FOR A GIVEN ARX MODEL SYSTEM IDENTIFICATION 79-84 Saa Prodanovi, Vesna Brai

COMPARING THE RESULTS OF STOCHASTIC APPROXIMATION METHOD WITH AVERAGING 85-91 RELATED TO CONVENIENT IDENTIFICATION METHODS Vesna Brai

ROBUST RECURSIVE IDENTIFICATION OF MULTIVARIABLE PROCESSES 93-98 Vladimir Djordjevic, Vojislav Filipovic

SESSION E: MECHANICAL DESIGN AND MECHANICS GEAR DRIVE UNIT WITH CONTINUAL VARIATION OF TRANSMISSION RATIO 1-6 Sanja Vasin, Milosav Ognjanovic, Marko Milos

CAD MODEL OF DISC BRAKE FOR ELIMINATING NOISE PROBLEMS 7-16 Jasna Gliovi, Jovanka Luki, Dobrivoje ati, Vanja uteri

INFLUENCE OF SUB-STRUCTURES SHAPES ON VIBRATION BEHAVIOUR OF SANDWICH 17-22 WALLS Aleksandar Vrani, Sneana iri Kosti, Bojan Tati

NUMERICAL-EXPERIMENTAL IDENTIFICATION OF A WORKING UNIT MODULE DYNAMIC 23-28 CHARACTERISTICS Aleksandar Koarac, Milan Zeljkovi, Cvijetin Mlaenovi, Aleksandar ivkovi

THE USE OF VIRTUAL MODELS IN THE DESIGN OF MECHANISMS 29-34 Ivan Milievi, Stojan Savkovi, Milosav ekari, Radomir Slavkovi, Nedeljko Dui, Marko Popovi

CONTRIBUTION TO THE DETERMINATION OF THE LOAD ON SUSPENSION RING 35-39 OF THE UNDERFRAME OF THE HYDRAULIC EXCAVATOR Slavia alini, Marko Nikoli, Goran Bokovi

INFLUENCE OF PLASTICITY REDUCTION ON INTEGRITY AND SERVICE LIFE OF TURBINE 41-45 RUNNER COVER OF THE HYDROELECTRIC GENERATING SET A4 AT HYDRO POWER PLANT ERDAP Miodrag Arsic, Srdjan Bosnjak, Vencislav Grabulov, Brane Vistac, Zoran Savic

COUPLING OF BENDING IN HORIZONTAL PLANE AND TWIST OF A TRUSS BEAM 47-52 WITH TRIANGULAR CROSS-SECTION Milan Dedic, Milica Todorovic

FREIGHT WAGON MASS REDUCTION USING PARAMETRIC OPTIMIZATION 53-60 Marko Topalovi, Vladimir Milovanovi, Milan Blagojevi, Aleksandar Dii, Dragan Raki, Miroslav ivkovi

NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM OF CONSTANT THICKNESS 61-69 AND LINEARLY TAPERED WIDTH Aleksandar Nikoli, Slavia alini

AN ANALYSIS OF THE END DEFLECTIONS OF SPATIAL TRUSSES WITH RIGIDITY VARIABLE 71-76 IN INTERVALS Milica Todorovic, Milan Dedic

SHAPING THE HOUSING OF TRANSMISSION GEAR WITH HIGH SPECIFIC POWER 77-82 Vojkan Nojner, Dragan Mili

SESSION F: RAILWAY ENGINEERING THE WAVE DISTORORTION ANALYSIS OF THE VOLTAGE FOR CONTACT LINE SYSTEM 1-7 AT SERBIAN RAILWAYS Branislav Gavrilovic, Zoran Bundalo, Savo Gavrilovic

DEVELOPMENT OF KEY PERFORMANCE INDICATORS FOR MAINTENANCE OF THE RAILWAY 9-12 SIGNALLING SYSTEM Margarita Georgieva, Nelly Stoytcheva

EFFECTIVE STRATEGY FOR MAINTENANCE OF THE RAILWAY ASSETS 13-19 Nelly Stoytcheva, Margarita Georgieva

APPLICATION OF GPSS QUEUING NETWORK MODEL TO EVALUATE THE PERFORMANCE 21-26 OF THE TRANSPORTATION TECHNOLOGICAL SYSTEM Kiril Karagyozov

WEB BASED SYSTEM FOR THE INTEGRATION OF THE OVERHAUL PROCESS FOR RAILWAY 27-32 BRAKING DEVICES Zdravko Tei, Branislav Stevanov, Danijela Graanin

IMITATION MODEL OF DISPATCHING SYSTEM FOR CONTROL ON PROCESSES 33-39 IN METROPOLITAN-SOFIA Emiliya Dimitrova, Vasil Dimitrov

OPTIMIZATION OF FREIGHT WAGONS FLEET OF REPUBLIC OF BULGARIA 41-46 Valeri Nikolov, Boris Galev

INFLUENCE OF THE DESIGN OF BRAKE DISCS ON THE THERMAL EFFICIENCY 47-50 Vasko Nikolov

INFLUENCE OF TRACK SUBSIDENCE ON ROLLING STOCK DERAILMENT RISK 51-58 Dobrinka Atmadzhova, Tsvyatko Penchev

A CRASH BUFFER FOR RAILWAY VEHICLES 59-68 Venelin Pavlov, Dobrinka Atmadzhova

VALIDATION OF A RAILWAY VEHICLE MODEL BASED ON COMPARISON OF CUMULATIVE 69-76 DISTRIBUTION FUNCTIONS Neboja Bogojevi, Jelena Tomi, Slobodan Todosijevi, Vojkan Luanin

FUNCTIONS OF WHEEL-RAIL CONTACT GEOMETRY 77-84 Milan Bii, Dragan Petrovi, Isidora Pani

NUMERICAL SIMULATION OF WAGONS IMPACT 85-92 Dragan Petrovi, Milan Bii, Dragan Pani, Dragi Mirkovi

METHOD OF CONTROL OF THE TRAIN MOVEMENT BASED ON NATURAL RECUPERATION 93-96 OF ENERGY V. A. Shevchenko, V. Kh. Pshikhopov, M. Yu. Medvedev, A.R. Gaiduk, A. A. Zarifyan, Yu. P. Voloschenko

SESSION G: URBAN ENGINEERING, THERMAL TECHNIQUE AND ENVIRONMENT PROTECTION MONITORIZATION SYSTEM FOR THE ENVIROMENT IN THE PROXIMITY OF INDUSTRIAL 1-6 POLLUTERS USING A SINGLE-BOARD COMPUTER RASPBERRY PI Cristina Sescu-Gal, Mihail Savaniu

EFFECT OF THE SUSPENSION ON WHOLE BODY VIBRATION: COMPARISON OF HIGH POWER 7-11 AGRICULTURAL TRACTORS Boban Cvetanovi, Miljan Cvetkovi, Dragan Cvetkovi, Milo Risti

INVESTIGATION AND REDUCTION OF NOISE GENERATED BY HEAVY TRAFFIC 13-18 IN URBAN ENVIRONMENT Vasile Bacria, Nicolae Herisanu

RECONSTRUCTION OF WAREHOUSE SYSTEM IN PHARMACEUTICAL INDUSTRY 19-24 Dusan Petrovic, Ugljesa Bugaric, Zoran Petrovic

PERSPECTIVE OR AIRLINE DEVELOPMENT, THE CASE OF KONSTANTIN VELIKI 25-30 AIRPORT NI Vojislav Tomi, Goran Petrovi, Danijel Markovi, Milo Madi

APPLICATION OF CORRELATION TEST TO CRITERIA SELECTION FOR MULTI CRITERIA 31-36 DECISION MAKING PROBLEMS IN DOMAIN OF LOGISTICS SYSTEMS Goran Markovic, Zoran Bogicevic, Mile Savkovic, Zoran Marinkovic, Vojislav Tomic

DEVELOPMENT OF MICRO COGENERATION PLANTS IN INDIVIDUAL HOUSES 37-44 Jelica Dimitrijevi, Stefan Pantovi

DEVELOPING MODEL OF A PHOTOACOUSTIC MEASUREMENT SYSTEM 45-50 Slobodan Todosijevi, Slobodanka Galovi, Jelena Tomi, Zlatan oki

DEVELOPING METHODOLOGY FOR THE SELECTION OF PRIORITY LOCAL INFRASTRUCTURE 51-54 PROJECTS TO BE IMPLEMENTED IN SPECIFIC PLANNED PERIOD Jovan Nesovic, Mirko Djapic

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SIMPLIFIED MODELING OF ELECTRICAL CABINETS 61-68 Rade Karamarkovic, Vladan Karamarkovic, Miljan Marasevic, Andjela Lazarevic

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PLENNARY SESSION

VIII International Conference Heavy Machinery-HM 2014, Zlatibor, 25-28 June 2014, P.1-8

*Corresponding author: Universitatea tehnic de construci Bucureti and [email protected]

Modelling and Working Simulation of the Mechanism of Axial Piston Hydrostatic Pumps Using Denavit - Hartenberg Method

Adrian Bruja1, Marian Dima1 1 Technical University of Civil Engineering of Bucharest, Bucharest (Romania)

The Denavit - Hartenberg method is one of the most frequently used methods for studying spatial bar mechanisms. Having in mind that this method can be used for open chain spatial mechanisms, it was used very often for studying the positioning and orientation mechanisms of robots.

In this paper is presented an overview of the method and an application to kinematics study of 2 types of axial piston pumps. Keywords: Denavit-Hartenberg, mechanisms, spatial bar, open chain, robots, axial piston pumps

1. METHOD OVERVIEW In this method to every kinematic element is

attached a reference frame according to the Denavit - Hartenberg [3] convention. For the open loop kinematic chain composed of consecutive kinematic elements i-2, i-1, i and i+1 and the kinematic joints linking the elements, Figure 2, the choosing of the reference frames linked to the elements i-1 and i is carried out as follows:

1. Direction of the zi-1 axis that links the element i-

1 to i is the joints axis; 2. xi-1 axis is linked to the element i-1 and is

chosen to the common normal of the zi-1 and zi-2 axes oriented from Oi-2 to Oi-1;

3. Similarly the axis xi is chosen as common normal of the rotation axes zi-1 and zi oriented from Oi-1 to Oi;

4. The origins of the reference frames are chosen in the intersection points between the common normal and the axis of the revolute joint, respectively Oi-2 and Oi-1;

5. The name of the joint is given by the highest order of the elements that complete the joint.

The y axes are chosen so that the reference frame is orthogonal.

Figure 1.

The geometrical parameters which entirely describe the transition from a reference frame i-1 to a reference frame i are as follows:

Table 1.

i Is the joints angle from axis xi-1 to axis xi, measured counter clockwise, around axis zi-1

id

Is the distance from the origin Oi-1 to the intersection of the axis zi-1 with axis ix , measured along the axis zi-1

ia Is the distance from the intersection of the axis zi-1 with xi to the origin Oi, measured along the axis xi (or the least distance between zi-1 and zi axes)

i

Is the angle between the zi-1. axis with the axis zi,

by rotating it around xi axis counter clockwise. The transition from reference frame "i-1", attached

to the element i-1, to the reference frame "i", attached to the element i, is carried out as follows:

1. rotation zi-1 around axis by angle i, in order to overlap the xi-1 axis with xi; 2. a translation along the axis zi-1 with the distance di, which brings the origin Oi-1 in the intermediate position Hi-1 (Figure 1); 3. a new translation along the axis xi by the ai distance, thus overlapping the origin Oi-1 to Oi; 4. Finally a second rotation around axis xi by an angle i, in order to overlap zi-1 axis with zi. Each one of these 4 movements can be expressed

using an elementary rotation or translation matrix and the resulting movement being the product of the matrices:

1 1 1 1( , ) ( , ) ( , ) ( , )

ii i i i i i i i iT Rot z Trans z d Trans x a Rot x = (1) Doing the multiplication of the elementary matrices

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VIII International Conference Heavy Machinery-HM 2014, Zlatibor, 25-28 June 2014

A. Bruja, M. Dima

cos( ) sin( ) 0 0 1 0 0 0 1 0 0 1 0 0 0sin( ) cos( ) 0 0 0 1 0 0 0 1 0 0 0 cos( ) sin( ) 0

0 0 1 0 0 0 1 0 0 1 0 0 sin( ) cos( ) 00 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1

i i i

i i i i

i i i

a

d

(2)

The transition matrix from the reference frame "i-1", attached to the element i-1, to the reference frame "i", attached

to the element i, is obtained

1

cos( ) sin( ) cos( ) sin( ) sin( ) cos( )sin( ) cos( ) cos( ) cos( ) sin( ) sin( )

0 sin( ) cos( )0 0 0 1

i i i i i i i

i i i i i i iii

i i i

aa

Td

= (3)

The said transition matrix (3) sets the position and

orientation of the reference frame "i", attached to the element i in relation to the reference frame "i-1", attached to the element i-1.

In this matrix the first 3 columns represent the direction cosines of the reference frames axes Oi in relation to the reference frame axes Oi-1, meaning the orientation of the reference frame Oi in relation to the Oi-1 reference frame and the 4th column the position of the Oi centre in relation to Oi-1. 2. BUILDING THE FORWARD KINEMATIC MODEL

FOR THE MECHANISM OF THE AXIAL PISTON HYDROSTATIC PUMPS

In Figure 2a, 2b are presented the working scheme of 2 types of axial piston hydrostatic pumps. In the case presented in Figure 2a the pistons block is rotating along with the disc and the driving shaft, while in the Figure 2b the pistons block and the disc have the rotation about the AC axis blocked and the driving shaft is rotating in relation to these around the C joint. In both cases between the pistons block and the disc, there isnt any relative motion in relation to the AC axis. The equivalent scheme from the pistons kinematics point of view, of the spatial bars mechanism, corresponding to the 2 types of pumps is presented in Figure 2c

Figure 2a.

Figure 2b.

Figure 2c.

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2.1. Applying the Method for Kinematics Study of a Point D Over the Discs Periphery

For the study, is taken into consideration the spatial

mechanism ACDF, Figure 2c. The kinematic scheme of this mechanism is equivalent from kinematic point of view to the scheme in Figure 3.

2.1.1. Attaching the Reference Frames According to the 2 the kinematic scheme in Figure

3 is analysed. In this case the z axes of the reference frames will be: z0 for the element 0, z1 for the element 1, respectively z2 for element 2 and z3 for element 3.

Figure 3. Figure 4.

Axis x1 is perpendicular on axes z0 and z1 and the

origin of the reference frame O1 is at the intersection between the axes x1 and z1, point C. The axis x2 is perpendicular on axes z1 and z2 and the origin of the reference frame O2 is still in point C (intersection between the axes x2 and z2). The axis x3 is perpendicular on axes z2 and z3 and the origin of the reference frame O3 is again in point C (intersection between the axes x3 and z3). The reference frames are presented in Figure 4. For easier expressing of the transfer matrixes O1, O2, O3 the origins are considered as in Figure 3 with the condition 1 2 0O O =

and 2 3 0O O = .

2.1.2. Modelling the Displacements of Point D

As shown in 2, in case of Denavit - Hartenberg method, the transition from one reference frame i-1 to a reference frame i is done using the transfer matrix 1

ii T ,

equations (1,2). In case of the ACDG mechanism, Figure 3, i = 1...

3 and the transition from a reference frame to another is carried out in the joints A(01), C(12) and D(23).

The geometrical parameters that describe the transfer from a reference frame to another, according to.2, Figure 1, are i, di, ai, i. For the ACDG mechanism these are presented table 1 for every joint.

Table 2.

Joint i id ia i Variable

iq A (0-1) 1 d 0 - 1 C (1-2) - 2 0 0 -/2 2 D (2-3) 3 -/2 0 0 /2 3

Starting from equation (2) based on the parameters in table 1 the transition matrixes are obtained 1

ii T for

transition from one reference frame to another in case of the studied mechanism.

The matrix 0T1

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A. Bruja, M. Dima

1 1 1 1

1 1

cos( ) sin( ) 0 0 1 0 0 0 1 0 0 0 1 0 0 0 cos( ) cos( )sin( ) sin(sin( ) cos( ) 0 0 0 1 0 0 0 1 0 0 0 cos( ) sin( ) 0

0 0 1 0 0 0 1 0 0 1 0 0 sin( ) cos( ) 00 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1

d

=

1

1 1 1

)sin( ) 0sin( ) cos( )cos( ) sin( )sin( ) 0

0 sin( ) cos( )0 0 0 1

d

(4)

the matrix 1T2

2 2 2 2

2 2

cos( ) sin( ) 0 0 1 0 0 0 1 0 0 0 1 0 0 0 cos( ) 0 sin(sin( ) cos( ) 0 0 0 1 0 0 0 1 0 0 0 cos( / 2) sin( / 2) 0

0 0 1 0 0 0 1 0 0 0 1 0 0 sin( / 2) cos( / 2) 00 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1

=

2 2

) 0sin( ) 0 cos( ) 0

0 1 0 00 0 0 1

(5)

the matrix 2T3

3 3

3 3

cos( / 2) sin( / 2) 0 0 1 0 0 0 1 0 0 0 1 0 0 0 sisin( / 2) cos( / 2) 0 0 0 1 0 0 0 1 0 0 0 cos( / 2) sin( / 2) 0

0 0 1 0 0 0 1 0 0 0 1 0 0 sin( / 2) cos( / 2) 00 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1

=

3 3

3 3

n( ) 0 cos( ) 0cos( ) 0 sin( ) 0

0 1 0 00 0 0 1

(6)

Forward model 0T3 = 0T11T22T3

1 1 1 2 2 3 3

1 1 1 2 2 3 3

cos( ) cos( )sin( ) sin( )sin( ) 0 cos( ) 0 sin( ) 0 sin( ) 0 cos( ) 0sin( ) cos( )cos( ) sin( )sin( ) 0 sin( ) 0 cos( ) 0 cos( ) 0 sin( ) 0

0 sin( ) cos( ) 0 1 0 0 0 1 0 00 0 0 1 0 0 0 1 0 0 0 1

d

(7)

After calculating the product the transfer matrix 30T is obtained.

0 3 0 3 0 3

0 3 0 3 0 330

0 3 0 3 0 3

0 0 0 1 0 0 0 0

xx x x x

yy y y y

zz z z z

i i i j i k pn o a p

j i j j j k pn o a pT k i k j k k pn o a p

= =

(8)

where:

1 2 3 3 1 1 2 3cos( ) cos( ) sin( ) sin( ) cos( ) sin( ) cos( ) sin( ) sin( ) sin( )xn = + 1 3 1 2 3 1 2 3sin( ) cos( ) cos( ) sin( ) cos( ) sin( ) cos( ) cos( ) cos( ) sin( )yn = + 3 2 3cos( ) cos( ) sin( ) sin( ) sin( )zn = + 1 2 1 2cos( ) sin( ) cos( ) sin( ) cos( )xo = 1 2 1 2sin( ) sin( ) cos( ) cos( ) cos( )yo = + (9) 2sin( ) cos( )zo = 1 3 1 2 3 1 2 3sin( ) sin( ) sin( ) cos( ) cos( ) cos( ) cos( ) sin( ) sin( ) cos( )xa = 1 3 1 2 3 1 2 3sin( ) cos( ) sin( ) sin( ) cos( ) cos( ) cos( ) cos( ) sin( ) cos( )ya = + 3 2 3cos( ) sin( ) sin( ) sin( ) cos( )za = px = 0; py = 0; pz = d

In these equations, n, o and a are the direction

cosines of the reference frame O3 in relation to the reference frame O0, p position parameters of the O3 origin in relation to O0 and i , j and k are the unit vectors of the axes x, y and respectively z.

Taking into account the direction of the reference frames axes and the direction cosines, and the position parameters an equation system of 12 equations with 12 unknowns is obtained.

In case of ACDG mechanism known variables and 1. For the kinematics study of the point D needs to be determined 2 and 3.

In order to determine 2, knowing that the y3 is perpendicular on the axis x0, Figure 3, is considered in (8), direction cosine 0 3 0xo i j= = . Considering the value of

2 given by (9) the following equation is obtained 1 2 1 2cos( ) sin( ) cos( ) sin( ) cos( ) 0 = (10)

Results

2 2 1( , )f = (11)

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For determining 3 the axes z3 and z0, are considered perpendicular according to Figure 3. As consequence, from equations (8) we obtained

030 == kkaz . Taking into account the value of az from equations

(9) we get the equation of 3

3 2 3cos( ) sin( ) sin( ) sin( ) cos( ) 0 = (12)

Taking into consideration the equation (11) we obtain

3 3 1( , )f = (13) Determining the Paths of Points on the Periphery of the Disc

The points D are placed on a circle of radius r,

Figure 5, belonging to the disc 2, Figure 3, to which, through the spherical joints, are connected the bars DE, Figure 2, that transmit the movement of the pistons. These points are equally spaced, which depends on the pistons number, over the periphery of the circle of radius r.

By positioning a point D over the periphery of the disc the other positions are determined automatically. Out of these points, from kinematic point of view characteristic are the points D1 and D, Figure 5.

Figure 5.

Trajectory of the Point D1 The coordinates of point D1 related to the origin O0

are obtained from the equation

( )( )( )

( )( )( )

0 22

00 2

0 2

12

1 0

1

( )( ) 0( ) 0

D D

D D

D D

x xy T yz z

x ry Ty

=

=

(14)

Where the transition matrix 20T has the form 2 1 2

0 0 1T T T= , the product 1 2

0 1T T is in equation (7). From equation (14) we obtain:

1 1 2

1 1 2

1 1 2

( ) ( , , , )( ) ( , , , )( ) ( , , , )

x

y

z

x f ry f rz f r

=

=

=

(15)

2.1.3. Motion simulation for points D1 and D

The simulation was carried out for the following

initial data: d = 160mm, r = 80 mm, = 15 and = 30. Point D1

The results are presented in Figure 6a, for 15 =

and in Figure 6b for 30 = .

Figure 6a.

Figure 6b.

Point D

The trajectory of point D is a particular case of

point D1, the motion can be only in plane z0y0. The trajectory is a circle of radius r, z and by varying these parameters like in for the point D1 and y will have the values of x from point D1. In plane x0z0 the trajectory would be a line contained in plane z0y0.

The D1 trajectories are characteristic to axial piston pumps in Figure 2a , to which all the joints between the disc and the bars have identical trajectories with point D1.

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A. Bruja, M. Dima

The trajectories of type D are seen in axial piston pumps presented in Figure 2b and are characteristic to the bars on CDF axis, Figure 2c. To these pumps the trajectory is modified from an arc (D) to octoid (D1) for an apex angle of points D from 0 to /2, starting from D and from the octoid (D1) to an arc for an apex angle of /2 to (the point on axis CF opposed to D).

Figure 3. 2.1.4. The Influence of the Parametres Over the Trajectory

From equations (15) we can see that the trajectory

depens on 1, 2, , r, d. Having in mind that 1 is the varible and that 2 = f(1, ) and d doesn influence the trajectory, but soleley defines its position in relation to the origin O0, can be seen that the trajectory is influenced only by and r. Increasing the angle leads to the increase of the variation range of z, which in turn leads to the increase of the specific flow of the pump. The increase of angle leads also to the increase of y which leads to a higher increase of the trajectory length with influence over the velocities of points D.

The increase of radius r has an effect on increasing the variation range of z, with an influence over the specific flow, and an increasing of the variation range of x, having an influence over the velocities of points D.

2.1.5. Velocities Study for Points D1, D

By differentiating over time the equations (10) and

(12) the equations of the angular velocities of 2 and 3 are obtained

2 2 1 2 1( , , , )vf = ; 3 3 1 2 1( , , , )vf = (16)

By differentiating over time the equations (15) the

equations of the velocities components by the x, y, z axes are obtained

1 2 1 2

1 2 1 2

1 2 1 2

( , , , , , )( , , , , , )( , , , , , )

x xv

y yv

z zv

v f rv f rv f r

=

=

=

(17)

2.1.6. Accelerations Study for Points D1, D

By differentiating over time the equations (16) and

(17) the equations of the angular accelerations of 2 and 3, and also the equations of the accelerations components by ax, ay, az axes of points D.

2.2. Kinematics Study of Points E, Pistons Joints

2.2.1. Modelling The kinematics study of the pistons, points E,

Figure 8, is carried out through the closed contours method, which in this case is simpler to apply than other methods, having in mind that the kinematics of point D is already.

Figure 8. For the vector is in Figure 8 we have the condition

4

10i

is

=

= (18) In this vector equation there are 2 unknowns,

direction of the vector 2s , and the magnitude of the vector

3s , so the system is uniquely determined. By projecting the system (18) on the axes of

reference frame O0x0y0z0 and solving the system, the ordinate 1( , )Ez f = , is determined, the position of point E along he axis of the piston.

By successive differentiations over time of the equations zE, the equations of velocities and accelerations of point E, vE and respectively aE are obtained.

2.2.2. Simulation and kinematic diagrams

The simulation was carried out using the following

parameters: = 15, 1 = 0 2; d = 100mm; r = 40mm; DE = 50mm.

The diagram of the pistons displacements is presented in Figure 9.

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Figure 9.

The diagrams are presented for type tip a) pumps,

Figure 2. Variation range of the space is constant for all the pistons, as can be seen in Figure 9 and that, along with the pistons radius give the displacement of the pump. For type b) pumps, Figure 2, the variation range is the same as for type a a), so the displacement is the same. The small differences that appear in the variation of the diagrams is not influencing the pumps working.

In Figure 10 are presented the velocities of the 11 pistons in case of type a), Figure 2 for the following kinematic parameters: 1 62,8 /rad s = ;(tciclu = 0,1 s). As it can be seen for all the pistons the maximum value for the top dead position is the same, the resulting velocity being quasi-constant, and so the pumps flow. The unevenness degree is 4% . if the number of pistons is increasing, for the same radius r, decreases and vice versa.

Figure 10.

In Figure 12 the velocities diagrams are presented for the type b) pumps, Figure 2. In this case the unevenness is higher than for type a pumps. The unevenness degree is

10% . The velocity difference is due to the differences in pistons displacements (3.1.3, Figure 7) for the same amount of time.

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A. Bruja, M. Dima

Figure 11. Figure 12. The acceleration diagrams for type b) piston pumps are presented in Figure 12, = 628 rad/s2, tcicly = 0,1s

Figure 13.

REFERENCES

[1] Adrian Bruja, Marian Dima Studiul cinematicii mecanismelor convertizoarelor hidrostatice cu ajutorul calculatorului.. Al VI-lea Simpozion Internaional IFToMM, vol IV, pag. 9-16, 1-5 iunie 1993. Bucureti. [2] Michel Casin, Jeanine Metge Mecanique de la robotique. Dunod,1989 [3] Denavit J. and Hartenberg R. S., 1955, A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices, Journal of Applied Mechanics, pp. 215-221. [4] Fischer, I.S., Numerical analysis of displacements in spatial mechanisms with ball joints, Mechanism and Machine Theory, Vol. 35, pp. 16231640, 2000.

[5] Richard S. Hartenberg, Jacques Denavit Kinematic synthesis of linkages. McGraw Hill, 1964 [6] Raghavan M. and Roth B., 1993, "Inverse Kinematics of the General 6R Manipulator and Related Linkages," Journal of Mechanical Design,Transactions of the ASME., Vol. 115, pp. 502-508. [7] Anghel Raicu, Adrian Bruja. Mecanisme. UTCB, 1996. [8] Siciliano, B., s.a. Robotics. Modelling, Planning and Control, Springer, 2009. [9] Wolfram Stadler -Analytical robotics and mechatronics.McGraw-Hill 1995.

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*Corresponding author: National construction and architectures university of Harkov and [email protected]

Definition Rational Gate Frame Size Distribution Unit Double Piston Concrete Pump With Hydraulic Drive Inga A. Emeliyanova 1*, . A. Zadorozhny1, D. V. Legeyda 1, N. A. Melencov 2

1 National construction and architectures university of Harkov, Harkov (Ukraine) 2 OOO "Stalikonstrukciya" Harkov (Ukraine)

Analysed the existing design of substations concrete pumps with hydraulic drive. A new design of gate node concrete

pump. Models of movement viscoplastic fluids. The conditions for building a model of the motion of the concrete mix in the pipeline. A scheme for calculating the structural and technological parameters of gate distribution unit with a V-shaped channel concrete pump.

Keywords: Viscoplastic environment, Rheology model, Hydraulic concrete pump

1. INTRODUCTION Transport of concrete mixtures to construction site

where work is done, by rule is achieved by double-piston hydraulic concrete pumps and concrete auto-pumps. Depending on maximum size of aggregate grain, concrete pumps performance, cross section of transportation pipeline, the working cylinders will be different and by that also the constructive solution of slide rule splitting frame.

Process of charging the hydraulic concrete pumps while transporting the concrete mixture by pipeline, from the point of saving its original characteristics after the mixing, is always an actual problematics.

Existing constructive solutions of distributional device of modern concrete pumps are especially interesting. Thus, distributional device in the shape of letter S (Figure 1) [1] - is the most common type of working organ of concrete pump.

Pistons of concrete pump cylinders move in opposite phases related to each other. One of them sucks the concrete mixture into the working cylinder from the receiving hopper, and the other pushes it through the distributional device shaped as S, which is in the shape of return pipe for concrete transport.

Figure 1: Working organ with distributor in S shape firm

CIFA (Italy) 1 - slide rule in S shape; 2- wear compensation ring; 3- drain hole with limit switch; 4- receiving hopper

with mixer

S shaped slide rule is guided by the side-mounted small hydro-cylinders whose one end is connected to the cylinder for transport of mixture, and the other one is articulated with the tube for transport of concrete.

Between the cylindersends of concrete pump and distributor with S nozzle the slide rule rings are set, made of high quality steel, as well as the so called wear compensation rings.

Figure 2: Working organ with rock-slide rule, firm

Schwing (USA)

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I. A. Emeliyanova, . A. Zadorozhny, D. V. Legeyda, N. A. Melencov

Slide rule thickness varies, which contributes its almost complete wear protection. Lower slide rule part is stiffened by ribs that prevent cumulation of material deposit and easy flow of large particles.

Wear compensation ring is set between the slide rule ring and the distribution device that works in authomatic mode. So, the problem of slide rule rings thickness is eliminated, because after its wear, it is moved forward by compensation ring, in which way the need for constant regulation of this frame is eliminated.

Rock-slide rule (Figure 2), (firm Schwing, USA) [2] represents a hollow truncated equilateral cup smashed on one side in the middle by horizontal plane.

Undeformed end of rock-slide rule alternately conveys concrete mixture to hydraulic system toward the working cylindersends. Each of two smashedends is firmly leaned to the back wall of concrete transport tube that has stiffening-ribs for strong (direct) contact with concrete transport pipeline.

Slide rule that is made in C shape (Figure 3) constructively differs to distribution slide rule shaped in S (Figure 1). It is produced as a separate series of the firm Putzmeister AG (Germany) [3].

Figure 3: Concrete pump with C slide rule, Firm Putzmeister AG (Germany): 1-vehicle chassis; 2- hydrocylinder; 3-

concrete transport tube; 4- working cylinder; 5- C slide rule; 6- grid; 7- smasher; 8- receiving hopper

Articular slide rule (Figure 4) has the shape of a tube

whose one end alternately connects to transport cylinders and the other one is articulated with concrete transport tube [4].

Figure 4: Scheme of concrete pump with articulated slide rule

1- concrete transport tube; 2- hydrocylinder; 3- piston rod; 4- articulated slide rules swivel arm; 5- articulated slide rule; 6- hopper; 7- working cylinder; 8- working piston; 9- working cylinders piston rods; 10- hydrocylinder

Dispensing slide rule shaped as a lock that is slanting

(Figure 5), is a product of Chinese company Sani. Such slide rule is set on a stationary concrete pump Operation principle

of such dispensing slide rule is achieved by additional periodical forced moving of concrete mixture by worm

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Definition Rational Gate Frame Size Distribution Unit Double Piston Concrete Pump With Hydraulic Drive

mixer with vanes from receiving hopper into doser for dispensing with a lock.

Figure 5: Principle scheme of concrete pump by Chinese company Sani with slanting slide rule for dispensing and

with forced charging

On the base of analysis of existing concrete pumps constructions, with the aim of improving the concrete pumps productivity on account of reducing the stoppage during repairs and shortening the time of technical servicing, a new simplified constructive solution of hydraulic slide rule distribution frame has been elaborated, at the Department for Mechanization of Construction Processes on Harkov National University of Construction and Architecture.

Feature of new construction is the position of slide rule distribution frame (Figure 6). Distribution frame is set between the receiving hopper and working cylinders. Such solution has a channel shaped as V and has a possibility of shifting horizontally in relation to central axis of dispensing pipe [6].

Proposed constructive solution of concrete pump is patented and is currently produced in the company OOO Harkov.

Figure 6: Principle scheme of mixtures moving through channel V, of hydraulic concrete pumps slide rule distribution

frame

Concrete pump includes the receiving hoppers body 1 with frontal plate 2 and transient plate of pumps body 3, with holes 4. First working cylinder 5 and second working cylinder 6, are placed on the flange with holes on rear edge of concrete pumps body 7. In first and second working cylinder pistons move 8 and 9 with piston rods 10 i 11. Output flow tube 12 is placed on the flange in the central part of transient plate 3 of pumps body for concrete that comes out of the holes on frontal plate 2 of receiving

hopper of pumps body and leans on the frontal part of slide rule plate 13.

Between front and rear slide rule plate 14, along the guide 15 in horizontal direction moves the distribution frame whose channel is in shape V 20 with two holes 18 and 19, which are placed on the rings ends 16 and 17.

Since the concrete mixture is of medium viscosity, its moving along the pipeline is realised after coping with an initial friction force. Mechanical behaviour of concrete mixture and character of mass conveyance process are

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I. A. Emeliyanova, . A. Zadorozhny, D. V. Legeyda, N. A. Melencov

characterized by very specific features which have to be taken into consideration while making models of transport working processes.

For model development of mentioned process we should consider the results of researches made by . . [7,8]. In them the proposed model came out from widely applied rheological stiff-plastic viscous models, which has summarized most of the classical equations of rheological fluids:

.2 11

1

1

0ij

mn

m

m

n

ij AA

+= (1)

here is: 2 22 2

2

2 2

2 2 2du dv dw dv duAdx dy dz dx dy

dv dw du dwdz dy dz dx

= + + + +

+ + + +

(2)

where ij load tensor components due to friction; ij deformation rate tensor; ( ), ,u x y z , ( ), ,v x y z , ( ), ,w x y z concrete mixture particles movement components; ( ), ,x y z spatial coordinates; deformation rate intensity; 0 obtained mixtures movement tension; n rheological parameter, m plasticity parameter. Model (1) flexibly combines plastic and viscous properties of concrete mixture

Taking the concrete mixtures viscous-plastic environment, we should take into account that such mixtures are to be considered as fluids Swed-Bingham. Thereby the dynamic viscosity p for viscous-plastic fluid should be considered as a shift rate function ( ) .

If we bring the concrete mixture into the one-dimensional flow, we should pay attention to the following models: Swed-Bingham;

0 . = + (3) Shullman;

1 1

0[ ( ) ] .nn m

p = + (4) Thereby, in calculation-construction and engineering

practice there is room for application of empirical curves of flow for cylindrical pipe conductors, related to one another by integral characteristics such as pressure and flow: for pipelines of round cross section [9,10];

38 4 .

4P D u Qf f

L D R

= = (5)

where P pressure (pressure difference); L pipeline length and diameter (D = 2R); i medium rate per volume

loss of mixture flow Q, 24 Qu

R

= .

Relation 8 uD for concrete mixture as non-Newton

fluid in pipeline of round cross section coincides with movement rate along the pipeline wall.

Finally, for model making for concrete mixture moving along the pipeline, that flows into the two cylinder concrete pump, considering the specific conditions as a base, physical-mechanical properties of mixture, we adopt the generalized model of non-linear viscous-plastic fluid (Z.P. Shullman model), which, after a series of transformations and model simplifications (1), gets the form:

( )1 1 1

0 .n n n = + (6) This model generalizes the most used models lately,

which take the formerly mentioned values: Newton (0 = 0; m = 0), Sen-Venan, Swed-Bingham (m = n = 1), Bulkyi-Gershell (n=1), Browne, Ostwald-DeVilly (0 = 0), Keson (m=n=2) and others.

Based on the above mentioned, for determining the wall inclination angle , for V shape channel (Figure 6) the calculation scheme is shown, which enables to determine the constructive measures of slide rule distribution frame (Figure 7) for the case when concrete mixture from working cylinder of concrete pump is directed to the output port.

Figure 7: Calculation scheme of concrete mixture

movement h1 distance between the inclined walls of V shape channel and direction of conductor for concrete transport, h2 distance between the outer walls of working cylinders

For analysis of concrete mixture movement through the V shape slide rule channel we use the equations of motion continuity and motion quantity in cylindric coordinate system ( zr ,, ).

( ) ( )1 0r rF

rr r r

= = . (7) 2

2 2

2;r rpr rr

= = . (8) After the equation differentiation (7) by , and the

equation (8) by r, the equation system takes the following form:

2 32

2 2 2 3 ,r rp

r r r

= =

(9)

2 2

22 1 12 ,r r rp

r r r r rr

= = +

(10)

On the base of equalities of the equations left sides (9) and (10) for concrete mixtures motion rate determination

r through the right branch of V channel, we can set the following differential equations:

3 2

3 2 2 0,r r rr

r

+ =

(11)

which we can consider for the following conditions:

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Definition Rational Gate Frame Size Distribution Unit Double Piston Concrete Pump With Hydraulic Drive

( ) ( ) 0,, ==== rr rr Volume loss of concrete mixture per channels width

unit and pressure in V channel are defined as:

( )

{ }{ }

02 2

2

; ,

sin sin

sin cos 2 sin

r rQ r d r

Qr

= =

=

+

(12)

( ){ }

{ }2

2 22

0, 2 2

cos sin 1

sin cos 2 sinr

XrQp p

X

= +

+

(13)

where 0- is the pressure on the initial part of V channel (Figures 6, 7); X-even parts length; - current angle in the cylindric coordinate system; 2 - channels opening angle.

Side walls slope of slide rules channel is determined on the base of constructive parameters h1, h2, L (Figure 7).

1L xtg

h

+= . (14)

Constructive dimensions of distribution slide rule frame with V channel for various diameters of working cylinders and of the output diameter of concrete transport pipeline are shown in table 1.

Table 1. Constructive dimensions of distribution slide rule frame with V channel for various diameters of working cylinders and of the output diameter of concrete transport pipeline

Working cylinders diameter with taking the

wall thickness D1,

Internal diameter of working cylinder

D2,

Concrete transport pipelines diameter

with taking the wall thickness

d1,

Internal diameter of the concrete

transport pipeline d2,

- saucer-shaped valves opening

angle

grade 120 100 120 100 128-130 144 125 120 100 121-125 180 150 120 100 123-125 210 180 120 100 125 250 220 120 100 123-125 310 250 120 100 124-125

In this way, dependencies (12) and (14) can be used for

determining the given constructive dimensions of V shape channel, with taking its throughput capacity at working pressure of concrete pump, and start the designing of distribution slide rule device.

REFERENCES [1] . . , .. , .. , .. . General classification of hydraulic concrete pumps, Scientific papers collection, Series: Sector engineering, machine construction., Vol. 1 (31) : , 2012. pp. 75 81, 2012 (in Ukrainian) [2] . . Machines for production of construction materials. .: , pp. 488, 1999 (in Ukrainian) [3] .. Mechanical equipment of reinforced concrete factories- Kiev: High School.. pp. 311, 1986 (in Russian) [4] .. Monolithic concrete: Technology of production works. Strojizdat,. pp 447. 1981(in Russian) [5] http://www.sanychina.ru/betononasos/gidravlika/ [6] Pat. 104755 Ukraine MPK (20.14.01) F04B 15/00 Concrete pump/ .., .., .., ..; Submitter and beneficiary Harkov National University of Construction and Architecture, registration 24 October 2011, publishing 25 April 2013, .5.

[7] . ., Zadoron A.A., Melencov N.A.. Preconditions for study of concrete mixtures transport process by double-piston hydraulic pump, Scientific papers collection, Series: Sector engineering, machine construction., Vol. 2 (30). Poltava: PNTU, pp. 23 24, 2011 (in Ukrainian). [8] .. . ., .. Analysis of concrete mixture motion through pipeline when using the double-piston concrete pumps in accordance with the model Swed-Bingham, Corpus of V International Scientific and Technical Conference: Applied Hydraulics and Pneumatics Odessa: Globus-Pres, pp.121 122, 2013 (in Ukrainian). [9] . ., . ., .. Defining the concrete pumps productivity, arising from the analysis of concrete mixture motion through pipeline, All Ukrainian scientific and technical magazine Applied Hydraulics and Pneumatics 4 pp.8-9, 2012 (in Ukrainian) . [10] .. , .. , .. , .. Concrete pumps productivity dependence on transported construction mixture propoerties, Magazine Science in Central Russia - , pp. 9-15, 2013 (in Russian).

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VIII International Conference Heavy Machinery-HM 2014, Zlatibor, 25-28 June 2014 P.14


*Corresponding author: DIN Viale Risorgimento, 2 40136 Bologna and [email protected]

Mechanical Behaviour and Friction Evolution on Bolted Connections Dario Croccolo1

1DIN Department of Industrial Engineering, Alma Mater Studiorum, Bologna (Italy)

Bolted connections are widely used to join mechanical and civil structures, which, usually, need to be adjusted or changed during their service life. Well-known mechanical applications are, for instance, the connections among the components assembled on front motorbike suspensions as well as the joints between the wheel hub and the wheel rim of vehicles or even bridge structures. Modern engineering materials used as bolts or substrates (for examples aluminium alloys, titanium alloys and composite materials), produce significant modifications to the mechanical behaviour of mated parts since the friction coefficients are subjected to a dramatic evolution both during and after the first tightening operation. This occurrence leads to a wrong estimation of the actual initial load applied to the screws and, as a consequence, to the connected parts. Furthermore an incorrect selection of bolts could be carried out due to the wrong estimation of actual stress field produced on bolt. In this paper the friction coefficient evolution and the mechanical behaviour of bolted joints have been deeply investigated in order to predict the stress field generated on the connected parts.

Keywords: Bolted connections, Friction coefficients, Mechanical behaviour 1. LOADS RELATIONSHIP ON BOLT CONNECTIONS

1.1. ISO geometry and loads equilibrium In the case of a metric standard (ISO M) profile, the

thread longitudinal section is an isosceles triangle with the thread angle of the screw equal to 60. According to the scheme of Fig. 1 it is, therefore, possible to relate the axial initial force Fi to the peripheral force Fp by means of the normal force FN and of the friction force.

Figure 1: Triangular thread: geometry and equilibrium of

forces The loads equilibrium along the vertical and

circumferential directions of screw, produce (1) in which the angle is the lead angle, the angle N is thread angle evaluated on the normal section of the thread (section A-A of Fig. 1) and the Tth is the torque moment applied to the thread.

(1)

Since tan()=p/(dm), (1) can be rewritten into (2).

(2)

The relationship between N and is expressed by

(3) in which dm= d2=d-0.64952p.

(3)

Equation (2) can be confidently approximated with very low errors into (4), which represents the actual relationship between the thread torque moment Tth and the initial load Fi for all the ISO screws.

(4)

1.2. Total torque moment acting on the threaded connections

Figure 2: Load scheme (axial and torsional) acting on the

screw during the tightening phase The whole threaded connection and, more

precisely, the bolt and the connected substrates, are involved by loads acting under the screw head that must be

P.15


D. Croccolo

take into account in order to calculate the total torque moment T to be generated by the torque wrench. As well indicated in the Figure 2, a considerable part of torque (Tunderhead=Tu and part of Tth) is consumed by the friction loads generated between the mating parts (the thread, the screw head and the substrates). The relationship between the total torque moment T and the initial load Fi is expressed by (5) in which u is the under-head friction coefficient and dA is the average value of the screw head diameter.

Equation (5) represents the basic formula to be used in order to relate the torque moment T to the initial force Fi. The stress field generated on the bolt depend on the initial force Fi and on the thread torque moment Tth; both of them are strongly affected by the friction coefficient and by the value of the screw head diameter dA. Especially in the case of high variation of coefficient of friction value, the (5) leads to high discrepancies in torque moment evaluation, provided that the Fi remains the same.

(5)

2. FRICTION COEFFICIENT EVOLUTION As well indicated in (5), the tightening torque

applied by the torque wrench, is mostly consumed in overcoming two friction components: the underhead component, generated by the sliding of the screw head on the flanges and the thread component generated by the sliding between the male and female threads. The residual torque component produces the fastener tension by generating the initial force. Inaccuracies in determining the friction values may lead to an overestimation or an underestimation of the bolted joint performances. The torque-load relationship is often simplified by using a constant K, known as torque coefficient or nut factor. The expression for the torque coefficient is reported in (6), where T Nmm is the input (total) tightening torque applied to the fastener, Fi N is the needed initial load and d mm is the nominal screw diameter following the ISO Standard.

(6)

In the case of screws, nuts and flanges made of

steel an effective value of K is 0.20 as suggested in [1, 2]. The present value is proved to remain constant for all the ISO screws if the value of friction coefficient remains equal to 0.14, but a large variation in K can be found if the friction coefficient changes. For this reason, some recent European Standards prescribe that the appropriate torque coefficient must be provided by the bolt manufacturer [3-5]. Bickford [6] indicates some mean values of the torque coefficient for various combinations of joint materials and surface conditions; however, the scatter is too great to provide a reliable and unique value, especially for critical joints and, furthermore, only steel screws are considered. The precise application of (6) is proposed by Motosh [7] and by VDI 2230 [8], but only in the case of bolt and substrates made of steel and in absence of lubrication between the mating parts the coefficients of friction and u are, usually, considered to be equal to a unique value named tot.

The effect of the variation of the coefficient of friction has been deeply investigated in [9-14]. In the case of an M8x1.25 bolt and of a mean value for friction coefficients m=tot equal to 0.15, it is easy to verify that 88% of the total input torque T is consumed in overcoming the friction loads [11]. Despite the fact that the majority of bolted joints in mechanical and civil systems are still realised with steel screws and steel substrates, many kinds of lightweight materials have been recently adopted for

screws and substrates construction [15, 16]. Since the use of threaded fasteners is considered worldwide to be an easy and simple way of joining components, sometimes designers do not take into account the changed boundary conditions, when replacing conventional steel screws and substrates with lightweight ones, or simply when replacing the surface finishing of bolted components. In [11] several failures occurred on clamped joints (Figure 3) due to the wrong estimation of friction coefficients have been examined. Two zinc plated steel screws acting on aluminium alloy have been investigated. The thread and the underhead regions could be anodized or spray-painted: the DOE methodology has been applied to determine reliable values for the friction coefficients (and therefore for initial loads estimation) involved in the joints, in order to avoid any type failures.

Figure 3: Failures occurred in clamped joints of a front

motorbike suspension

Figure 4: Specific specimens manufactured for retrieving

the friction coefficients

Special specimens reported in Figure 4 have been specifically manufactured in order to retrieve the friction coefficients by applying (7). Equation (7) results from (5) adopting the same coefficient of friction for the thread and underhead sliding surfaces.

(7)

P.16


Mechanical Behaviour and Friction Evolution on Bolted Connections

Figure 5: Torque wrench used for the esperimentation

The total torque T was obtained by a calibrated torque wrench illustrated in Figure 5, whereas the initial load Fi=FV was evaluated by means of a strain gauge, located on the external surface of the specimen reported in Figure 4, which is able to provide the axial compression strain C. The compression force FC (8) acting on the specimen is equal, in magnitude, to the initial force acting on the screw, since the system works like springs connected in series during the tightening phase. The innovative specimens are cheaper and easier to use than the most common friction machinery, based on displacement transducers, load cells, rotary torque sensors or angle encoders and DC motors [14, 17]. Furthermore, it is possible to avoid the application of strain gauges on the bolt (difficult to perform in the case of nominal diameters lower than 12mm) in order to measure the actual initial force. (8)

Figure 6: Bar diagrams of the friction coefficient m for

forged specimens ((a): spray-painted (b): anodized) in the case of tightening torque T=15Nm (different series for

lubricated and unlubricated specimens)

Figure 7: Bar diagrams of the initial load Fi for forged specimens ((a): spray-painted (b): anodized) in case of

tightening torque T=15Nm (different series for lubricated and unlubricated specimens)

The results condensed and collected in the bar

diagrams of Figures 6 and 7 have been obtained and analysed by applying the DOE method [18] and the Analysis of Variance (ANOVA) [18, 19].

It is evident that spray-painted specimens have the lower value of m=tot (the higher initial forces Fi=FV). In the presence of unspoiled surfaces, the overall friction coefficient decreases from a value of 0.26 in the case of forged, anodized and unlubricated specimens to a value of 0.11 in the case of forged, spray-painted and unlubricated ones, so that the initial force doubles with the same tightening torque T=15Nm. Lubrication always increases the initial forces: in the presence of forged and unspoiled surfaces, the overall friction coefficient decreases from a value of 0.11 to 0.08 in the case of spray-painted specimens, and from a value of 0.26 to 0.16 in the case of anodized ones. Finally, considering the effect of the number of tightening and loosening (up to six maintenance operations in a standard lifecycle) the initial force is affected by the tightening replicas mainly in the case of unlubricated and anodized surfaces so that the Fi progressively decreases with the same tightening torque. As a matter of fact surfaces are subjected to wear and spoiling (Fig. 8) by increasing the number of tightening, while lubrication creates a sort of protective film. In the presence of spoiled surfaces, the overall friction coefficient increases from a value of 0.26 to 0.39 in the case of forged, anodized and unlubricated surfaces,

P.17


D. Croccolo

whereas a value of 0.16 to 0.17 is observed in the case of forged, anodized and lubricated surfaces.

Figure 8: Spray-painted specimens (a): unspoiled surfaces

(b): spoiled surfaces The same outcomes have been observed by

changing both bolt and substrate materials. For instance another experimentation has been conducted in the case of titanium screws connected to aluminium substrate in order to replicate the joint between the wheel rim and the wheel hub similar to the sketch reported in Fig. 9, which is a typical connection adopted for wheels of sport cars.

Figure 9: Car wheel assembly with titanium screw

Figure 10: Specific specimens manufactured for retrieving

the friction coefficients In this case, since the investigation has been

dedicated to analyse the friction coefficient evolution by changing the number of tightening and the type of

lubricant, the specimens were designed and specifically manufactured in order to share the key parameters of the actual components involved in the wheel-rim joint.

The results of the present investigation are collected in the Figures 11, 12 and 13.

Figure 11: Friction coefficient tot (mean, maximum and

minimum values) versus tightening number for DRY surfaces

Figure 12: Friction coefficient tot (mean, maximum and

minimum values) versus tightening number for EP Plus oil lubricated surfaces

Figure 13: Friction coefficient tot (mean, maximum and minimum values) versus tightening number for HT1200

paste lubricated surfaces

The important role played by lubrication in order to reduce and to control the evolution of the coefficients of friction, is extensively evident having a quick look at the results reported into the following diagrams. The lowest

P.18



and most constant value, has been obtained when the HT1200 paste is applied, whereas in the case of dry surface, the highest value reached by the friction coefficient, produces an initial force notably lower than that predicted for the same torque moment. In some cases the high friction forces produced under the head of screws, lead to undesirable failures, which are well highlighted on the screw head reported in the Fig. 14.

Figure 14: Titanium screw assembled on an aluminium

test specimen (left) and failure of the hexagon socket head The underhead coefficients of friction have been,

also, analysed separately respect to the thread ones in order to point out the friction phenomena occurring during the tightening phase [20]. If friction is investigated, the characteristic values of pressure and sliding velocity are fundamental to be analysed. Fig. 15 shows an example of underhead contact parameters useful for the assessment of tribological behaviour. During the assembly phase the sliding velocity, with a linear radius-distribution, is generated by the rotation of the bolt or of the nut, which produce pressure inhomogeneities. Pressure peaks are generated both by detailed support geometry of components in contact and by the local stiffness of parts [21]. A rough approach evaluates the mean values of the present parameters (pm, vm and dm), anyway by doing this some unusual situations can be pointed out especially in the case of different and innovative materials in contact.

Figure 15: Key parameters for the tribological assessment of bolted joints at head support

For example if different materials for screws ((I)

steel, (II) titanium and (III) aluminium) are coupled with different materials for substrates ((i) steel, (ii) aluminium, (iii) magnesium and (iv) CFRP) such as the samples reported in Fig. 16, some unusual outcomes, well highlighted by the diagrams of Fig. 17, can be observed

and commented concerning the evolution of the friction coefficients.

The overall (tot) friction coefficient trends, reported in Fig. 17, indicate a significant reduction in values when the torque and the initial load increase. The same behaviour has been observed for the underhead friction coefficients that have been separated by mean of the specific torque machine and tools used for the tests and reported in Fig. 18.

Figure 16: Screws and substrates types

Figure 17: Total friction coefficient diagram for different

substrates with aluminum screws unlubricated

Figure 18: Multi channel testing tools and machine

radius of contact r(lever arm for local friction forces, influenced by concave/convex contour of screw head support geometry)

tightening angle

speed vmean

and local vmin, vmax(dependent on radius of support area)

contact pressure pcclocal, pccmean(dependent on magintude of support area Ah and preload level Fp, possibly inhomogeneous distribution)

pccmean = FpAh

axis of rotation (fixed)

(responsible forsliding distance and wear)

fund

amen

tals

...ds

f

vmean = n ( dw + da)

2

Ah = (dw - da )4 2 2

dw da

Fp

0,00

0,00

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0 2 4 6 8 10

CFRP (vi) Steel (i)

Aluminum (ii)

Magnesium (iii)

h = 0,05

h = 0,13

h = 0,03

h = 0,11

h = 0,89 h = 0,61

h = 0,85 h = 0,43

Preload FP0 [kN]

Tota

l fric

tion c

oeffi

cient

tot

0 20 40 60Contact pressure under head psteel (i) [N/mm2]

0 20 40 60Contact pressure under head paluminum (ii) [N/mm2]

0,000 20 40 60

Contact pressure under head pmagnesium (iii) [N/mm2]80

0,000 20 40 60

Contact pressure under head pCFRP (vi) [N/mm2]

P.19


D. Croccolo

Figure 19: Sliding surface damage after fifth tightening

procedures

Doubtless the values of friction coefficient cannot decrease so much and moreover they cannot be so high as those calculated, for instance, in the case of CFRP substrate (h=0.89) with a so large variation during the tightening phase. Since the coefficient of friction values have been calculated by applying (7) and by relating the torque moment to the initial force, their evolution can be influenced by the variation of the pressure distribution and, accordingly, by the variation of the underhead mean diameter. As a matter of fact the sliding surfaces of different substrates assumed different aspects and geometric configurations after the damage due to five tightening operations, as well indicated in the pictures of Fig. 19. Even if it is, actually, important to know the value of friction coefficient corresponding to the torque moment or to initial load applied, the evolution or change of friction forces must be taken into account for the correct selection of bolts and for the stress definition of involved parts.

3. FRICTION COEFFICIENT IMPORTANCE FOR THE

BOLT SELECTION AND STRENGTH The correct definition of friction coefficient values

of the actual connections is dramatically important for the bolt selection and strength [22]. Depending on the type of external loads (shear loads, bending moments and torque moments), the forces can be represented by the generic scheme reported in Fig. 20.

For a correct selection, the bolt must be clamped with an initial force Fi (9), which is able to guarantee the transmission of the aforementioned forces (as a general design rule the use of a safety factor is suggested to magnify the external loads). The tension load Rn can be directly equated with a part of Fi, whereas shear load Rt is transmitted via the friction developed among plates by assuming a coefficient of friction equal to p and by applying the Coulomb law in order to relate Rt to Fi.

(9)

Figure 20: Forces acting on the bolt

The design methodology, which leads to the

selection of an appropriate screw, must take into account the elastic behaviour of the bolt-plates system, in particular in presence of external tensile loads. The initial load (Fi) definition is only the first issue for the screw designers that must, then, guarantee the entire life service of joints: therefore the connections must support the initial load as well as the external loads, without producing any kind of failure during all the expected life of the product. For this reason, the attention has to be also dedicated to the study of working loads and failure modes. The well-known force-displacement diagram [6], reported in Fig. 21 is useful to assist this study.

Figure 21: Force-displacement diagram

In brief, during the initial tightening phase the bolt

(B) and the plates (P) share the same initial force Fi (the system works as series of springs), to which corresponds different variations in length due to different stiffness. Once the components are clamped, an external load parallel to the bolt axis (Rn), produces an increase of the tension (FB) acting on the bolt as well as a decrease of the pressure (FP) acting on the plates: the amounts of FB and FP are proportional to the total external load Rn depending on the stiffness of two components (the clamped members work as a parallel of springs because they share the same displacement). The accurate definition (10) of the maximum tensile load FB acting on the screw is important in order to select the appropriate screw.

P.20



(10)

The dimensionless parameter C used in (10) and defined by (11) is called load factor and results as a function of bolt (KB) and plates (KP) stiffness.

(11)

The calculation of the load factor performed via FEA, is well described in a paper by Cornwell [23] (see also [24-26]) for different materials and geometrical configurations: the main conclusion is that the load factor, for practical applications and in presence of different materials of plates, can be assumed in the range 0.1-0.45 for steel bolts.

The maximum static load acting on the bolt is, therefore, given by the combination of the previous (9) and (10) to obtain the following equation:

(12)

In addition to the maximum tensile force FB, the torque moment Tth given by (4) acts on the screw body during the tightening phase.

According to the Von Mises yield criterion it is possible to calculate the equivalent axial load EQ acting on the bolt (13): the axial stress ax is equal to FB/At whereas the maximum torsional (shear) stress t is equal to Tth/Wt (the stress area At and the torsional modulus Wt are calculated using dt diameter, equal to the average between the minimum d3 and the mean d2 diameters of the screw, (dt=d-0.9382p).

(13)

The equivalent axial load depends both on the

assembly conditions (initial force and thread coefficient of friction), and on the service conditions (load factor and external loads). In order to select the appropriate screw it is necessary to verify that EQ results lower than the Yield point of material p0.2 or lower than the stress under proof load Sp (Sp 0.9 p0.2 according to ISO898). EQ depends on (i) the external loads Rt and Rn, (ii) the thread friction coefficient (t) and the plate friction coefficient (P), (iii) the load factor C, and (iv) the bolt dimensions (p, d2 and dt): therefore, in order to select the bolt, it is necessary to know the bolt dimensions as well, so that the right choice needs at least one iteration. For this reason, according to EC3 [27] (13) can be simplified into (14) in the case of steel plates considered much more rigid then the bolt (C0) and assuming a standard value of thread coefficient of friction t =0.15.

(14)

At this point an interesting issue could be to analyse the trend of the stress ratio SR=EQ/i as a function of the following parameters:

The bolt nominal diameter (M6M24); The coefficient of friction between plates p

(0.11); The thread coefficient of friction t (0.11); The load factor C (0, 0.25, 0.5 and 0.75); The value of Rt and Rn. As a matter of fact during the tightening phase C

parameter is equal to 0 so that (13) results equal to (15).

(15) The trend of SR as a function of the bolt dimension

has been analysed, by changing the ratio between Rt and Rn and by fixing the value of the friction coefficients (p=0.2 and t=0.15). SR values, reported in Fig. 22, are within 1.32 (M6) and 1.26 (M24) values for all the analysed dimensions, whatever are the values of Rt and Rn: therefore the bolt dimension does not affect the SR value sensibly with discrepancies within 5%.

Figure 22: SR as a function of the bolt size for different

values of Rt/Rn

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D. Croccolo

Figure 23: SR as a function of p for different values of

Rt/Rn Since the bolt dimension does not affect

significantly the value of the SR, it is possible to select a bolt size (for instance M12) and to analyse the variation of SR as a function of the coefficient of friction between the plates, by changing the ratio between Rt and Rn, for a fixed value of the thread coefficient of friction (t=0.15). In this case the value of SR is constantly equal to 1.3 as well indicated in Fig. 23.

Figure 24: SR as a function of t for different values of

Rt/Rn In the case of variation of t the SR value

dramatically changes as shown in Fig. 24 so that the value of 1.3 could be no longer valid to assure the right selection of bolts. Whatever are the values of Rt and Rn, SR increases almost linearly with the thread coefficient of friction. SR always exceeds the value of 2 starting from thread friction coefficients values within 0.3 and 0.4 since the torsional contribution assumes a predominant role. It is important to highlight that the use of lubricated screws produces low values of coefficient of friction almost in every conditions, also in replicated tightening operations as well demonstrated in [11-13]: the values are always lower than 0.17.

4. CONCLUSION

The mechanical behaviour of bolted joints is strongly affected by the friction coefficients evolution. The possibility and capability to control the coefficient of friction values during the tightening operations is strategically important for the right selection of bolts

especially in the case of modern connection

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