Impulsinių apkrovų veikiamos netiesinės dinaminės sistemos Neįgalus žmogus - vežimėlis - transporto priemonė judesio stabilumo tyrimas ; Motion stability analysis of the nonlinear dynamic system Man - Wheelchair - Vehicle under action of impulsive loads
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Julius GRIŠKEVI ČIUS MOTION STABILITY ANALYSIS OF THE NONLINEAR DYNAMIC SYSTEM “MAN – WHEELCHAIR – VEHICLE” UNDER ACTION OF IMPULSIVE LOADS Summary of Doctoral Dissertation Technological Sciences, Mechanical Engineering (09T) 1177 Vilnius 2005 VILNIUS GEDIMINAS TECHNICAL UNIVERSITY Julius GRIŠKEVI ČIUS MOTION STABILITY ANALYSIS OF THE NONLINEAR DYNAMIC SYSTEM “MAN – WHEELCHAIR – VEHICLE” UNDER ACTION OF IMPULSIVE LOADS Summary of Doctoral Dissertation Technological Sciences, Mechanical Engineering (09T) Vilnius 2005 Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2001 – 2005 Scientific Supervisor Prof Dr Habil Me čislovas MARI ŪNAS (Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering – 09T) The Dissertation is being defended at the Council of Scientific Field of Mechanical Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Mindaugas LEONAVI ČIUS (Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering – 09T) Members: Prof Dr Habil Rimantas BELEVI ČIUS (Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering – 09T) Prof Dr Habil Vladas VEKTERIS (Vilnius Gediminas Technical University, Teiences, Mechanical Engineering – 09T) Prof Dr Habil
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Julius GRIKEVIČIUS MOTION STABILITY ANALYSIS OF THE NONLINEAR DYNAMIC SYSTEM MAN WHEELCHAIR VEHICLE UNDER ACTION OF IMPULSIVE LOADS Summary of Doctoral Dissertation Technological Sciences, Mechanical Engineering (09T)
Vilnius
2005
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VILNIUS GEDIMINAS TECHNICAL UNIVERSITY Julius GRIKEVIČIUS MOTION STABILITY ANALYSIS OF THE NONLINEAR DYNAMIC SYSTEM MAN WHEELCHAIR VEHICLE UNDER ACTION OF IMPULSIVE LOADS Summary of Doctoral Dissertation Technological Sciences, Mechanical Engineering (09T)
Vilnius 2005
Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2001 2005 Scientific Supervisor Prof Dr Habil Mečislovas MARIŪNAS(Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering 09T) The Dissertation is being defended at the Council of Scientific Field of Mechanical Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Mindaugas LEONAVIČIUS(Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering 09T) Members: Prof Dr Habil Rimantas BELEVIČIUS (Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering 09T) Prof Dr Habil Vladas VEKTERIS (Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering 09T) Prof Dr Habil Algimantas FEDARAVIČIUS University of (Kaunas Technology, Technological Sciences, Mechanical Engineering 09T) Prof Dr Habil Petras ILGAKOJIS University of (Lithuanian Agriculture, Technological Sciences, Mechanical Engineering 09T) Opponents: Prof Dr Habil Genadijus KULVIETIS Gediminas Technical (Vilnius University, Technological Sciences, Mechanical Engineering 09T) Assoc Prof Dr Rymantas Tadas TOLOČKA University of (Kaunas Technology, Technological Sciences, Mechanical Engineering 09T) The dissertation will be defended at the public meeting of the Council of Scientific Field of Mechanical Engineering in the Senate Hall of Vilnius Gediminas Technical University at 2 p. m. on 27 October 2005. Address: Saulėtekio al. 11, LT-10223 Vilnius-40, Lithuania Tel.: +370 5 274 49 52, +370 5 274 49 56; fax +370 5 270 01 12, e-mail doktor@adm.vtu.lt The summary of the doctoral dissertation was distributed on 27 September 2005 A copy of the doctoral dissertation is available for review at the Library of Vilnius Gediminas Technical University (Saulėtekio al. 14, Vilnius, Lithuania) © Julius Grikevičius, 2005
VILNIAUS GEDIMINO TECHNIKOS UNIVERSITETAS Julius GRIKEVIČIUS IMPULSINIŲAPKROVŲVEIKIAMOS NETIESINĖS DINAMINĖS SISTEMOS NEĮGALUS MOGUS VEIMĖLIS TRANSPORTO PRIEMONĖ JUDESIO STABILUMO TYRIMAS Daktaro disertacijos santrauka Technologijos mokslai, mechanikos ininerija (09T)
Vilnius 2005
Disertacija rengta 2001 2005 metais Vilniaus Gedimino technikos universitete. Mokslinis vadovas prof. habil. dr. Mečislovas MARIŪNAS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos ininerija 09T). Disertacija ginama Vilniaus Gedimino technikos universiteto Mechanikos ininerijos mokslo krypties taryboje: Pirmininkas prof. habil. dr. Mindaugas LEONAVIČIUS(Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos ininerija 09T). Nariai: prof. habil. dr. Rimantas BELEVIČIUS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos ininerija 09T), prof. habil. dr. Vladas VEKTERIS Gedimino technikos (Vilniaus universitetas, technologijos mokslai, mechanikos ininerija 09T), prof. habil. dr. Algimantas FEDARAVIČIUS (Kauno technologijos universitetas, technologijos mokslai, mechanikos ininerija 09T), prof. habil. dr. Petras ILGAKOJIS(Lietuvos emėsūkio universitetas, technologijos mokslai, mechanikos ininerija 09T). Oponentai: prof. habil. dr. Genadijus KULVIETIS Gedimino technikos (Vilniaus universitetas, technologijos mokslai, mechanikos ininerija 09T), doc. dr. Rymantas Tadas TOLOČKA technologijos (Kauno universitetas, technologijos mokslai, mechanikos ininerija 09T). Disertacija bus ginama vieame Mechanikos ininerijos mokslo krypties tarybos posėspalio 27 d. 14 val. Vilniaus Gedimino technikosdyje 2005 m. universiteto senato posėdiųsalėje. Adresas: Saulėtekio al. 11, LT-10223 Vilnius-40, Lietuva. Tel.: +370 5 274 49 52, +370 5 274 49 56; faksas +370 5 270 01 12, el. patas doktor@adm.vtu.lt Disertacijos santrauka isiuntinėta 2005 m. rugsėjo 27 d. Disertaciją galima periūrėti Vilniaus Gedimino technikos universiteto bibliotekoje (Saulėtekio al. 14, Vilnius, Lietuva) VGTU leidyklos Technika 1177 mokslo literatūros knyga © Julius Grikevičius, 2005
GENERAL CHARACTERISTIC OF THE DISSERTATION Topicality of the problem Nowadays disabled persons are actively integrated into social life. Different compensatory equipment allows them to work and travel independently. The wheelchair is one of such means; it provides mobility function for physically impaired persons. Not every disabled person has possibilities to travel by his own car and sometimes there is no necessity to use the car in the city, where the intensity of traffic is high. It is more convenient to use public transport facilities, for example bus or trolleybus. Wheelchair-bound passengers transportation safety is one of the most important problems facing transit providers and engineers. Improperly or totally unsecured wheelchair can lose the stability and tip over during the emergency driving situations and result in passenger falling and becoming injured. Standard wheelchair tie-down occupant restraint systems are not installed in all public transport and are often difficult to reach, uncomfortable to wear, and time-consuming to use and do not function properly. Hence there is a need for additional, simplified wheelchair restraint system that is safe, comfortable, and easy-to-use and allows independent usage for wheelchair-bound passengers. Aim and tasks of the work the main object of the scientific research work is complex dynamic system Man Wheelchair Vehicle, which is under action of environmental factors (road roughness, motion oscillations of vehicle). The main tasks of the work are: • to form and research non-linear model of dynamic system Man Wheelchair Vehicle and to define systems stability limits, to provide means for safe travel; • to determine main characteristics of the external action and analyze its influence on to considered dynamic system; • to build engineering computation methodology for estimation of the rational parameters to fasten the wheelchair to the vehicle. Scientific novelty • Nonlinear model of dynamic system Man Wheelchair Vehicle proposed enables to analyze motion stability and to determine critical limits of systems stability; • Investigated spectral density and its intensity of vehicles external action on the wheelchair during different driving regimes, like steady motion and emergency braking situations, on road with different pavement; • influence of wheelchair fastening characteristics on toAnalyzed wheelchair stability during the motion of vehicle;
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• Build simple computation methodology, which enables to select rational parameters of wheelchair fastening to the vehicle depending on disabled person stature and weight. Methodology of research analytical, experimental and statistical methods were used in scientific research work to achieve set tasks. LaGrange energy method was used to build two mass 12 degrees of freedom non-linear mathematical model of disabled person in a wheelchair was developed. Equations of motion were solved using numerical Runge-Kutta method, which algorithm was built in MATLAB environment. Experimental measurements of accelerations in three directions during the different driving regimes of public transport in Vilnius and Kaunas (two passenger buses Mercedes and Solaris Urbino) on different road state (dry, wet and snowy pavement) were performed using tri-axial accelerometers and portable Bruel&Kjaer equipment. The center of gravity of disabled person in a wheelchair was calculated using anthropometric data tables. Stiffness characteristics of wheelchair tyres were measured using loads and deformation indicators. The results of measurements data were processed using correlation analysis. Practical value • Nonlinear model of dynamic system Man Wheelchair Vehicle was proposed, which enables to analyze the stability of the wheelchair during the steady motion and emergency driving conditions of the vehicle, revealing non-stable motion velocities and dangerous acceleration values; to analyze spectral density of external action and its relation with the natural frequencies of wheelchair-seated disabled person; to diminish negative effects by selecting rational parameters of wheelchair and wheelchair fastening. • Created simple computation methodology enables to select rational parameters for wheelchair fastening to the vehicle. Defended propositions • Presented nonlinear model of dynamic system Man Wheelchair Vehicle allows to determine the stability limits of the wheelchair and dangerous acceleration values which occur during the motion of the vehicle, and to estimate external actions influence onto dynamic system. • Given engineering computation methodology allows to select rational wheelchair fastening to the vehicle parameters. The scope of the scientific work. The scientific work consists of the general characteristic of the dissertation, 4 chapters, conclusions, list of
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literature, and addenda. The total scope of the dissertation is 94 pages, 62 pictures, 13 tables. STRUCTURE OF THE WORK The first chapter gives a review of scientific research works on transportation safety of wheelchair-seated passengers. Analysis of the system Man Vehicle Environment was performed describing relations between people and vehicles they operate, traffic and environmental conditions. Evolution and comparison of different mathematical models Man Vehicle, which describe and analyze accidental situations was presented. Various wheelchair fastening systems used in transport mean nowadays were reviewed. The main tasks of the scientific work were formulated at the end of the chapter. The second chapterpresents the development of non-linear model of dynamic Man Wheelchair Vehicle system. The case when disabled person sits in his wheelchair during short-trip through the city using public transport was considered. The most common manual rear-wheel-driven wheelchair was chosen and two mass 12 degrees of freedom simplified dynamical model of dynamic system Man Wheelchair Vehicle (MWV) shown in Figure 1 was developed. The wheelchair is connected to the vehicle through elastic constraints in one point F with coordinatesht andLt. The disabled person is bound by elastic constraints only to the wheelchair.
Fig 1.The dynamical model of the wheelchair-seated disabled person
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(1)
Particular systems behavior cases were summarized and three possible situations were determined: the steady motion regime when the loads are small, the partial and complete abruption cases when as a result of loads increase the wheelchair tyres loose the contact with the vehicles ground. Vertical displacement z2 of the wheelchair inOz direction and the angle of angular displacement φ2about theOyare the basic parameters for the evaluation ofaxis dynamic system MWV stability in considered case. These parameters are bundled with the value of static deformation between the wheelchair tyres and the vehicles groundzstby the following expressions which describe previously mentioned three behavior cases of dynamic MWV system: ⎧12+L2pϕ2≤and2−L2pϕ2≤ ⎨⎪⎪⎪2.. zz2±LL2pϕ2>zzttandzz2∓LL2pϕ2≤zzsstt,, ⎪⎩3. z2+2pϕ2>ztandz2−2pϕ2>zst, whereLpis the distance between the wheels of the wheelchair. The equations of systems motion were obtained using LaGrange energy method. When the transport mean is driving under the steady regime of motion (case 1 in expression (1)), forces of kinematic or other excitation sources are moderate. Thus, vibrations in the dynamic system MWV will be small and the system of equations can be simplified assumingsin(φ,γ,ψ)≈ φ,γ,ψandcos (φ,γ,ψ)≈ but the increase of oscillations will make them significant. 1, Consequently, system of 2nd order non-linear differential equations describes the motion of the dynamic MWV system. It consists of two subsystems: first subsystem (2) describes the linear displacements in vertical, horizontal and forward directions and, taking into account simplifications made, the rotational motion of the system about the0x,0y,0z axis is described by the second subsystem (3) of non-linear differential equations: ⎪⎪⎪⎪⎧mmm111yxz111+++ccc654zxy111−−−ccc654zxy222+++kkk654zx1y11−−−kk5k46zx2y22===00,0,, ⎨⎪⎪⎪mm22xy22++((cc31++cc64++44cc98))xy22−−cc64x1y1++((kk31++k4k6++44k8k9))x2y2−−k4k6x1y1==F1F(2t()t,), ⎪⎩m2z2+(c2+c5+8c7)z2−c5z1+2c7Liγ2+(k2+k5+8k7)z2−k5z1+2k7Liγ2=F3t),
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(2)
⎧⎪I1y−m1hϕ2(HC1−h) (1+ϕ1ϕ2)ϕ1−m1ϕ1ϕ2h(HC1−h) (ϕ2−ϕ1) + ⎪⎪⎪⎪⎪+=IcQ14(−h2mH+Ch1cγ−5hL2Hϕ)ϕ11,−ch4h2+cγ5Lγ2ϕ2γ+km4γh2+hk5HL2ϕ1−kh4hγ2+kγ5h2ϕ2= C ⎪⎪⎪⎪⎪+1xc5L1u2+L2u2(i+C1c6−h2)γ(11+−c512L)u2+1L−u2i1+1cγ26h2(γ2+1−k5)L(2u+2−L2ui1)++k6h2γ1− −k5L2u+L2ui+k6h2γ2= −Q1LC1γ1, Izc L2L2c L2c L2L2c L2 1ψ1+4u+ui+6ψ1−4u+ui+6ψ2+ ⎪⎪⎪⎪⎪⎪+k4Lu2+Lu2i+k6L2ψ1−k4Lu2+Lu2i+k6L2ψ2=0, ⎪I2y+m1h2−m1hϕ1HC1−h1+ϕ1ϕ2ϕ2−m1ϕ1ϕ2hHC1−h(ϕ1−ϕ2) + ⎪⎪⎨⎪⎪⎪+c1ht2+c2L2xt+c4h2(+c5L2)+21(c7L2pϕ2)−c4h2+c5L2ϕ(1)+(3) ⎪⎪⎪⎪+k1ht2+k2L2xt+k4h2+k5L2+12k7L2pϕ2−k4h2+k5L2ϕ1= =(Q1h+Q2HC2)ϕ2+F1(t)ht+F3(t)Lp, ⎪⎪I2x+m1h2−m1+chγ1(HLC+1L−h(+)c1h+ γ1γ+2c)Lγ2γ−m1γ−1cγ2hL(H+CL1−h+c) (hγ1γ−γ2)++ ⎪+c2Lt2+c3ht2 5 2ui2u6247i2 2 5u2i u2621 2 2 2 2 2 2 2 2 2 ⎪⎪⎪⎪+k2Lt+k3ht+k5Lui+Lu+k6h+4k7Liγ2−k5Lui+Lu+k6hγ1= 2( ) (t t2) (1 2)C2 ⎪⎪⎪I=zFψt+hcL2++LcγL2−+cQ+LQ2i+LLu2,+c L2+1c Li2+1c L2pψ− 2 2 1t3xt4u 2 9 46 2 8 ⎪⎪2 2ψ−k Lui+Lu+k Lψ + 4 6 ⎪⎩⎪⎪+−kc1Lt2Lu+ik+3LL2utx++ck4LL2u2i+1Lu2+4k26L2+221k8Li62+24k19L2p2=F1(t)Lt+F2(t)Ltψ2, 1 whereF1,F2andF3are forces of external excitation,Q1andQ2are weight of the man and the wheelchair respectively, andI1x,y,z andI2x,y,z are moments of inertia of the man and the wheelchair respectively aboutOx,OyandOzaxis.
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When one of the conditions 2 or 3 in expression (1) are satisfied, the tyres of the wheelchair lose the contact with the vehicles ground and the wheelchair is restrained only at one fastening point. Thus, the frame of reference changes, a set of elastic constraints intermit and the motion of the dynamic Man Wheelchair Vehicle system is described by additional systems of non-linear differential equations. The third chapter presents the methodology of experimental measurements of vehicle motion characteristics and statistical processing of obtained data. Dynamical loads, which occur during the motion of vehicle, are caused by acceleration, which was recorded using tri-axial accelerometer and portable Bruel&Kjaer PULSE Type 3560C equipment. Figure 2 shows diagrammatically setup of experimental measurements.
Fig 2.Setup of experimental measurements: 1 accelerometer; 2 portable data acquisition system; 3 PC with analysis software Measurements were performed in two passenger buses Mercedes Benz O-305 and Solaris Urbino; the latter was low-floored, with rearward-facing compartment equipped with restraint belt for wheelchair-seated passengers. During daily routes of the public transport in city specific and frequently repetitive motion regimes were noted. They were: the start of moving and stopping in bus-stops, in traffic jams, high radius turnings, different maneuvers and so on. Accelerations, which affect the disabled person in the wheelchair during different bus driving regimes, were recorded and graphs of acceleration pulses, which depict the magnitude of dynamical loads, are shown in Figure 3.
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