OSCILLATIONS OF PARTIALLY FILLED TANKER TRUCK AT ITS BRAKING

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1 ENGINEERING FOR RURAL DEVELOPMENT Jegava, OSCILLATIONS OF PARTIALLY FILLED TANKER TRUCK AT ITS BRAKING Aexandr Shimanovsky Bearusian State University of Transport Astract. A significant part of iquids in agricutura production is transported y road tanks. Moving with iquid cargo is a compex dynamic system and specia attention shoud e paid to the reative dispacement of cargo, which can ead to oss of staiity and controaiity of the car. The main purpose of the work is to anayze the infuence of spring stiffness and whee weight on partiay fied tanker truck osciations at raking. The mathematica modeing of the road tank transported iquid cargo was performed. It was ased on the scheme, which considered the transported iquid as a soid ody that interacts with the tank through the viscoeastic connection with the noninear dependence of the eastic force on the cargo reative movement. Based on the numerica soution of the differentia equations for the tank motion the infuence of the cargo reative movement on the automoie stopping distance, as we as friction etween the whees and the road at the tank raking were anayzed. Cacuations showed that for the tank without affes there is an aternation of friction with and without siding. This can cause osses of car controaiity and overturning. The performed anaysis confirms that there is a need of transverse affe instaation to ensure tank controaiity at emergency raking. These partitions aow to damp iquid cargo osciations quicky or to ensure the est possie iquid cargo energy dissipation. Keywords: tanker truck, iquid cargo osciations, raking, forces of friction, sipping. Introduction In agricutura production there is a need of constant iquid cargo transportation. At the paces of tank fiing reservoirs are fied y the maxima aowed eve ut after some technoogica operations are performed the fiing eve of the tanks decreases. For exampe, this fact takes pace whie dispensing iquid cargoes for consumers. At the same time, it is possie to increase the fiing eve of the tank reservoir after operations at severa specia stations. Therefore, due to agricutura operationa needs the moving road tank is often partiay fied with iquid. The risk of a dangerous situation increases during the transportation process of such road tank. This is due to the fact that the vehice dynamic characteristics change ecause of the comparaiity of the empty tank weight with the iquid cargo weight and these characteristics are aso different from a fuy fied or an empty vehice []. The maxima mechanica stresses appear in the fuy fied tanks []. As for the case of partiay fied tank movement the greatest practica interest is the study of the tank dynamic characteristics at transient movement modes, ecause of the increasing proaiity of an accident. Traditionay, in the modes of road tank motion, rocket and space apparatus, marine tankers and others vehices and equipment iquid was modeed y equivaent mechanica modes [3-5]. Parameters of such equivaent systems can e determined on the asis of the study of iquid sma osciations in the tank. Such osciations can e approximatey taken into account at cacuation of vehices y the use of an equivaent mechanica mode consisting of a concentrated mass, associated with the vehice ody y inear eastic couping means. However, this mode does not consider osciation damping caused y iquid cargo wave dispersion and viscosity. So, it can e ony appied to the anaysis of reservoirs with one or severa separate compartments of reguar geometric shape. The author of the work [6] notes that the dissipative forces must aso e taken into account in the cacuation schemes, ut the investigators aso offer to determine these forces experimentay for each case. In the ast few years there was carried out a numer of studies ased on the performed finite eement modeing of iquid osciations in a moving tank [7-0]. However, these investigations did not considered possie sipping etween the vehice whees and the road. The computations incuding anaysis of friction in the vehice-road system can e impemented in the software package MSC.ADAMS [], ut in this case there can difficuties appear in determining the causes of different dynamic effects due to the ig amount of the mode parameters, which may e presented either in the form of graphs or taes. The paper [] demonstrates cacuation resuts for the raking process of a road tank. These cacuations are ased on the anaysis of a simpified mode of a tank with iquid cargo, as a system with two degrees of freedom and unaccounted whee weight. The resuts of the cacuations aowed to 56

2 ENGINEERING FOR RURAL DEVELOPMENT Jegava, find that short-term periodic sipping of the tank whees caused y cargo osciations can e oserved during tank emergency raking. This can cause oss of the car contro and appearing of a dangerous situation. The aim of the present work is to determine the features of the friction forces changes etween the whees and the road for the case of tank raking using on a more compex mode and taking into account the tank ody osciations on the springs and inertia of whees. Tank truck mathematica mode For the anaysis of tank raking trucks at its motion aong the horizonta surface the anayzed system was considered as a system incuding the tank ody, whees of the front and rear axes, the transported iquid. The moving part of iquid cargo can e determined from the formuas given in [6]. The cacuation scheme is shown in Fig.. Fig.. Scheme of the tank with equivaent iquid cargo In the scheme and further text the foowing symos are used: m, m, m, m weight of the tank ody, front and rear axes respectivey, kg; I, I, I moments of inertia of the tank ody, the front and rear axe respectivey, kg m ; x, z coordinates of the tank ody center of mass at its motion reative to the earth, m; s coordinate of the iquid cargo center of mass in the reative motion, m; the eginning of its counting corresponds to the position of cargo equiirium inside the tank, so it corresponds to the deformation of the eastic connection etween the cargo and ody; ϕ, ϕ, ϕ rotation anges of the tank ody and whees of the front and rear axe respectivey, rad; car ase, m;, distance from the rear axe to the tank ody and cargo centers of gravity in the equiirium position respectivey, m; h, h vertica coordinates of the tank and cargo centers of gravity respectivey, m; G, G, G gravity forces of the tank ody, front and rear axes respectivey, N; M f, M f moments generated y the front and rear axe rakes, N m; F f, F f friction forces etween the whees of the front and ack axes and the road, N; N, N norma reaction of the road for the front and ack axes, N; X, X horizonta interaction forces etween the axes and the vehice ody, N; F s, F s forces in the springs of front and rear axes, N; F ed resutant force of the iquid-tank ody interaction, N; F x, F z, F x, F z projections of ody and cargo forces of inertia on the axis x and z, N; 57

3 ENGINEERING FOR RURAL DEVELOPMENT Jegava, F i, F i front and rear axe forces of inertia, N; M i, M i, M i moments of inertia forces of the tank ody, front and rear axes respectivey, N m. The forces in the springs are connected with the tank ody movement y the dependencies: F c z + ( ) ); F c z ). () s= ( s ϕ s= ( s ϕ To account for the viscous resistance forces of iquid cargo its mass is connected to the reservoir y the viscoeastic eement. In this case, the interaction force etween the cargo and wa F ed can e represented as the sum of two terms: the eastic and dissipative component of the interaction force F ed = cs+αs&. () where c coefficient determined y the shape of the tank and the fiing eve; it is invoved to consider the effects of iquid movement on the tank ody ce and it can e determined as c= c 0 s s0 3( s s) max if s s0, c= c0e if s> s0, c 0 vaue of the coefficient c for the case of iquid sma osciations [6], N m - ; s 0 coordinate s, when iquid reaches the ce, m; s max coordinate s, for the case when a iquid cargo is ocated near one of the sides of the tank ody and its free surface is vertica, m; α coefficient aowing to take into consideration iquid osciation damping in the road reservoir, kg s -. The dot over the variae here and further denotes the derivative cacuated y time. Formua (3) is otained y the approximation of the cacuation resuts of iquid cargo osciations in road tanks [3] and showed good agreement with the experiment [4]. Equations for the inertia forces can e in the foowing view: Fx = m& x, Fz = m& z, Fx = m (&+ x& & s ), F = m (& z ( s) ϕ& z ), F m & i = x, F m & i = x. (4) Moments of inertia forces: M i= I ϕ&, M i = Iϕ&, M i = Iϕ&. (5) The ange ϕ is considered to e very sma, so sin ϕ = ϕ, cos ϕ =. Then, in accordance with the D Aemert principe the movement of the tank and reativey moving iquid cargo with taking into account reations (4) and (5) is descried y the foowing equations: F ed m && x X m && z+ m (&& z ( M f + M f m (&& s+ && x) + F X = 0. + X ϕ F ed s) ϕ&& ) + F s s + G + F s x h F + G ( z Equations for motion of the front and rear axes m && x X + F m && x X where r tire radius. N s I ϕ&& + M f f f r= 0; N F s I ϕ&& + M + s) + F f f F z f ( r= 0, + s) x h I ϕ= && 0; At road tank raking there is possie a situation of whee rotation aong the road with and without sipping. Therefore, it shoud e noted that in genera case the static friction force vaue for the ocation etween the tire and the road may not exceed the production of the friction coefficient and road norma reaction F f fn, fn (3) (6) (7) F f. (8) 58

4 ENGINEERING FOR RURAL DEVELOPMENT Jegava, Likewise, when the disk rakes operate, the maxima torques M max and M max can e reached ony when there is sipping of inings aong the rake discs. These torques have the pointed vaues according to the technica characteristics of rakes on the front and rear whees of the car. At the skidded whee motion there can e a situation, when the raking torque is ess than the maxima vaue, so the foowing conditions must e satisfied M f M max, M max M f. (9) Thus, cacuation of the road tanker raking is ased on the soution of differentia equations (6) and (7) considering the reations ()-(4), (8) and (9). Further cacuations performed in the MathCAD environment showed that the presence of inequaities (8) and (9) eads to inadequate resuts of the generaized acceeration cacuation or the divergence of noninear equation system soution on separate time intervas using the uit-in function Find. It turned out that this situation is caused y the noninearity appearing due to the need to adjust the friction force vaues for two cases. The first case corresponds to the motion with sipping, the second case without sipping. The proem was soved y using the uit-in function Minerr. It differs from Find in that, if the chosen agorithm fais to converge, whatever answer found on the ast aowae iteration is returned. Resuts and discussion On the asis of the presented dependences the cacuations were performed of the ased on the MAZ chassis road tank. Mode parameters were taken in accordance with the paper []. Maxima raking torques in the chassis rake pads are taken М max = 7000 N m for the front axis and М max = 800 N m for the rear axis. The cacuation resuts show that for the coefficient α equa to kg s - the changes in the raking distance do not exceed %. This resut is fuy consistent with the resuts of cacuations with zero whee mass []. Taking into account the spring deformation and mass of the whees did not ead to a significant change in the parameters of the iquid cargo osciations. Coefficient α has the greatest infuence on the movement and veocity of the iquid cargo center of mass (Fig. ). If the vaue of this coefficient is more than 0000 kg s -, the iquid cargo motion ecomes aperiodic. These vaues of the named coefficient can e achieved y interna perforated affe insta [5]. a) ) 0.6 s, m s, m t, s t, s Fig.. Reative veocity of iquid cargo centre of mass for: a α = 0000 kg s - ; α = 0000 kg s - Cacuations performed taking into account the mass of the whees and spring deformations confirmed the previousy otained resut for the simpified mode []. At ow vaues of the coefficient α (tank without affes) there is an aternation of tank movement modes with and without sipping. Consideration of additiona factors eads to a significant change in the dependence of the friction force of the front whee on time and it appears ony when the whees move with sipping (Fig. 3). For the rear whees considering of their mass aows to specify the nature of the dependence of the friction 59

5 ENGINEERING FOR RURAL DEVELOPMENT Jegava, forces on time ecause the cacuations for the simpified mode demonstrated a constant vaue of these forces under the infuence of the wide range of the factor α (Fig. 4). 35 a) ) F f, kn 5 F f, kn t, s t, s Fig. 3. Friction forces for the front whees at α = 5000 kg s - : a cacuations without considering the whee mass; cacuations with taking into account the whee mass 5 F f, kn t, s Fig. 4. Friction forces for the rear whees at α = 5000 kg s - : cacuations without considering the whee mass; cacuations with taking into account the whee mass The performed anaysis demonstrated that the incusion of the car spring deformation insignificanty affects the vaue of the friction force changes. The changes in friction force vaues are connected with the modes of the whee movement with and without sipping and can cause disturances of the car controaiity and its overturning. Furthermore, due to the friction hopping pushes the driver working conditions ecome worse. An increase in the coefficient α (corresponds to the tank with interna affes) eads to the smooth changes in the frictiona forces. Thus, the performed anaysis confirms that there is a need of transverse affe instaation to ensure the tank controaiity at emergency raking. These partitions aow to damp iquid cargo osciations quicky or to ensure the est possie iquid cargo energy dissipation. For the cases, when it is impossie to insta perforated affes in the existing road tank constructions, it is recommended for drivers to use partia (smooth) raking to reduce the osciation ampitudes of iquid cargo in the partiay fied reservoir. This wi aow to avoid the motion of whees with sipping. Concusions. The performed anaysis showed that compication of the mode descriing osciations of a tank partiay fied with iquid does not ead to significant changes in the resuts of the motion kinematic parameters and forces in the road-whee contacts. 60

6 ENGINEERING FOR RURAL DEVELOPMENT Jegava, It was approved that at movement of the tank without partitions the reative dispacement of iquid cargo eads to aternation of friction modes with and without sipping, which eads to a decrease of drivaiity and controaiity of the road tank. 3. Instaation of the partitions damping iquid cargo osciations heps smooth the changes of the friction forces and it aows to reach a significant improvement of the raking conditions. References. Высоцкий М.С., Плескачевский Ю.М., Шимановский А.О. Динамика автомобильных и железнодорожных цистерн (Dynamics of automoie and raiway tanks). Minsk: Beautotractorostroenie, p. (In Russian).. Lengvarsky P., Pástor M., Bocko J. Static Structura Anaysis of Water Tank. American Journa of Mechanica Engineering, vo. 3, 05, pp Dai L., Xu L., Setiawan B. A new non-inear approach to anayzing the dynamic ehavior of tank vehices sujected to iquid soshing. Proceedings of the Institution of Mechanica Engineers, Part K: Journa of Muti-ody Dynamics, vo. 9, 005, pp Deng X., Tait M. J. Equivaent mechanica modes of tuned iquid dampers with different tank geometries. Canadian Journa of Civi Engineering, vo. 35, 008, pp Ranganathan R., Yang Y. S. Impact of iquid shift on the raking characteristics of partiay fied tank vehices. Vehice system dynamics, vo. 6, 996, pp Dodge F.T. The new Dynamic ehavior of iquids in moving containers. San Antonio: Southwest Research Institute, p. 7. Chei F., D Aessandro V., Premoi A., Saioni E. Simuation of Soshing in Tank Tracks. Internationa Journa of Heavy Vehice Systems, vo. 0, 03, pp Liu K., Kang N. Simuation of iquid sosh in raking process of tank truck. Journa of Beijing University of Aeronautics and Astronautics, vo. 35, 009, pp Yan G., Rakheja S. Straight-ine raking dynamic anaysis of a party fied affed and unaffed tank truck. Proceedings of the Institution of Mechanica Engineers, Part D: Journa of Automoie Engineering, vo. 3, 009, pp Shimanovsky A., Kuzniatsova M., Sapietová А. Modeing of Newtonian and Non-Newtonian iquid soshing in road tanks whie raking. Appied Mechanics and Materias, vo. 6, 04, pp Sapietova A., Dekys V. Use of MSC.ADAMS software product in modeing viration sources. Communications Scientific etters of the University of Ziina, vo.8, No A, 06, pp Кузнецова М.Г. Анализ влияния перемещения жидкого груза в резервуарах цистерн на кинематические и динамические параметры автомобиля при торможении (Anaysis of iquid cargo movement in road tanks reservoirs infuence on the automoie kinematic and dynamic parameters at its raking). Topica questions of machine sciences: Актуальные вопросы машиноведения, 04, No 3, pp (In Russian). 3. Шимановский А.О. Модифицированная дискретно-массовая модель цистерны с жидкостью (Modified discrete-mass mode of tank with iquid). Mechanics, scientific researches and methodica deveopment: Механика, научные исследования и учебно-методические разработки, 0, vo. 5, pp (In Russian). 4. Gridnev S.Yu., Budkovoj A.N. Modeing of fuctuations of eam systems at the transitiona modes of the movement of vehices carrying iquids. Scientific Herad of the Voronezh State University of Architecture and Civi Engineering, Construction and Architecture, 05, No (6), pp Kuzniatsova M., Shimanovsky A. Definition of rationa form of atera perforated affe for road tanks. Procedia Engineering, vo. 34, 06, pp

PHYSICS LOCUS / / d dt. ( vi) mass, m moment of inertia, I. ( ix) linear momentum, p Angular momentum, l p mv l I

PHYSICS LOCUS / / d dt. ( vi) mass, m moment of inertia, I. ( ix) linear momentum, p Angular momentum, l p mv l I 6 n terms of moment of inertia, equation (7.8) can be written as The vector form of the above equation is...(7.9 a)...(7.9 b) The anguar acceeration produced is aong the direction of appied externa torque.