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International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 03, March 2019, pp. 172–177, Article ID: IJMET_10_03_017 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=3 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed NUMERICAL SIMULATION OF FREE AND FORCED OSCILLATIONS FOR PENDULUM TYPE CHILD TRAVEL SEAT N. L. Pavlov, E. E. Sokolov, M. H. Peychev and D. I. Dacova Department of Combustion Engines, Automobile Engineering and Transport, Faculty of Transport, Technical University of Sofia, 8 Kliment Ohridski Blvd., 1000 Sofia, Bulgaria ABSTRACT This paper presents a dynamic model of a tilting child travel seat. The child seat is presented as a physical pendulum. Thereby the seat in concert with the child can rotate around a cylindrical joint located above its mass center. This way the lateral acceleration acting on the child travelling in a cornering vehicle can be reduced. Thus the ride comfort of children travelling in road vehicles can be improved. The differential equation of motion of the system child-child seat, necessary for the needs of the research is presented. Numerical simulations of free and forced oscillations of the pendulum type child seat are carried out with MATLAB. Displacement, velocity and acceleration results obtained after conducting the numerical simulations are presented in graphical form. Key words: Dynamic model, child seat, pendulum and simulation Cite this Article: N. L. Pavlov, E. E. Sokolov, M. H. Peychev and D. I. Dacova, Numerical Simulation of Free and Forced Oscillations for Pendulum Type Child Travel Seat, International Journal of Mechanical Engineering and Technology 10(3), 2019, pp. 172–177. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=3 1. INTRODUCTION Passengers who travel in a vehicle passing through a curve at high speed sense the nature of the radial inertial force. Experiments have shown that an uncompensated radial (lateral) acceleration in excess of about 0,1g is definitely unpleasant [1]. This acceleration would be attained at about speed v=100 km/h on an 800 m radius curve (a=v2/r). One of solution is the superelevation of the track or road cross slope (virage). In addition to reducing the side thrust on the rails, superelevation tends to ensure that the resultant force of weight and inertia force is normal to the seat. Then if the superelevation is sufficient, there is no side force tending to slide the passenger across the seat. However, if a train moves slowly or stops in a curve, the internal rail is subject to considerable thrust or in the case of road vehicles - a slip on the road is possible. A second solution to the problem is to allow the body of the carriage to swing like a pendulum [1].This method is widely used in many high-speed trains to improve the ride http://www.iaeme.com/IJMET/index.asp 172 [email protected] N. L. Pavlov, E. E. Sokolov, M. H. Peychev and D. I. Dacova comfort [2]. The principle of inclination is also used in small narrow vehicles [3]. In trains there are passive and active tilting systems. There are no such structures in road transport. Instead of tilting the carriage or car (bus), seat-only tilt can be used [4]. The seat can be passive pendulum type. When a vehicle is cornering the centrifugal force tilts the seat and the lateral acceleration acting on travelling person is reduced. It will improve the ride comfort of people travelling in the vehicle. Given the fact that children are the most vulnerable group of kinetosis effects, a tilting child traveling seat can be used to improve the ride comfort of children traveling by car or by train. The aim of this paper is to demonstrate the effect of using a specially designed pendulum type tilting child seat on the free and forced oscillations by making a numerical simulation of a vibrating process. A dynamic pendulum model of the seat will be presented. Graphical results of the free and forced oscillations with given parameters will be shown and analyzed. 2. DESIGN OF A PENDULUM TYPE CHILD TRAVEL SEAT A 2D drawing with dimensions of an experimental prototype of a pendulum type child travel seat is shown in Fig. 1. Figure 1 2D drawing of an experimental prototype of tilting child seat As shown in the figure above, the seat in concert with the child can rotate around cylindrical joint located above its mass center. The seat is mounted by ball bearing on light metal frame. It is designed as an experimental prototype. If the tests prove that the seat is efficient and safe and if it enters in serial production, the frame can be made of polymer or carbon. The seat used in the prototype is made of polymer. The seat was taken from an existing non-tilting child seat model. 3. PENDULUM TYPE MODEL OF A CHILD TRAVEL SEAT The described tilting seat can be presented like a physical pendulum as shown in Fig. 3. The pendulum can rotate about a cylindrical joint. An angular damper with damping coefficient c is placed to reduce the additional high frequency oscillation. http://www.iaeme.com/IJMET/index.asp 173 [email protected] Numerical Simulation of Free and Forced Oscillations for Pendulum Type Child Travel Seat Figure 2 Equivalent pendulum type model of a tilting seat The differential equation of the pendulum free motion is: J x mgl sin c (1) where J x is an axle moment of inertia, about an axis of rotation passing beyond the body’s center of mass (non-central moment of inertia) [5]: J x J c ml 2 (2) where l is the distance between the axis crossing the center of mass and the axis of rotation (Steiner’s theorem); J c - moment of inertia about axis crossing the centre of mass; m - mass of the child-tilting seat system; c - angular damping coefficient; g - gravitational acceleration. The differential equation of the pendulum forced motion is: J x mgl sin c M (3) where M is the disturbance moment: M Fc l (4) v2 Fc m R (5) where Fc is the centrifugal force; v - vehicle speed; R - curve radius. http://www.iaeme.com/IJMET/index.asp 174 [email protected] N. L. Pavlov, E. E. Sokolov, M. H. Peychev and D. I. Dacova 4. NUMERICAL SIMULATIONS The simulations were performed using MATLAB with the parameters given in Table 1: Table 1 Simulation parameters Parameter Symbol Value Unit Mass of the child-tilting child seat m 10 kg system Distance l 0,28 m Moment of inertia about axis Jc 2,5 kg.m2 crossing the centre of mass Angular damping coefficient c var.* N.s/rad * - the angular damping coefficient can vary for simulations performed for tuning the system. The results of free oscillations simulations with three different angular damping coefficients are shown in Fig 3. Figure 3 Free damped oscillations of the pendulum with different damping coefficients The results show that if a small angular coefficient of 1 N.s/m is used the free oscillations are damped very slowly. If the coefficient c =10 N.s/m, the motion is aperiodic with fast damping (over-damping). Between them is situated the oscillation curve of damping with coefficient c =5 N.s/m. The forced oscillations simulations are performed with sinusoidal variation of the centrifugal force. This corresponds to the slalom motion of the vehicle. It is given by the following formula: Fc Fc max sin(t ) (6) where Fc max ma y 10.4 40 N; 1 rad/s 0,16 Hz is the frequency used in the simulations; a y 4 m/s2 is the lateral acceleration, taken from real slalom tests performed by the author and his science team and presented in the cited papers [6, 7]. The results are obtained by microelectromechanical inertial system (MEMS) consisting of sensors widely used in various fields of science and engineering in the recent years [8, 9]. The graphical results of forced oscillations simulations with the three different angular damping coefficients are shown in Fig. 4, 5 and 6. http://www.iaeme.com/IJMET/index.asp 175 [email protected] Numerical Simulation of Free and Forced Oscillations for Pendulum Type Child Travel Seat Figure 4 Angular displacement of pendulum forced oscillations with different damping coefficients Figure 5 Angular velocity of pendulum forced oscillations with different damping coefficients Figure 6 Angular acceleration of pendulum forced oscillations with different damping coefficients As can be seen in the last three figures above the angular displacement , the angular velocity and the angular acceleration have the smallest values in case of the bigger damping coefficient c . In the case of the lowest damping, additional harmonics of the speed and acceleration curves are noticed. They can reduce the efficiency of the system. As a result http://www.iaeme.com/IJMET/index.asp 176 [email protected] N. L. Pavlov, E. E. Sokolov, M. H. Peychev and D. I. Dacova the ride comfort can be disturbed. There is no significant difference between medium and high pre-damping case in simulations performed with the given parameters. 5. CONCLUSIONS The proposed model allows studying the system parameters impact on the kinematic parameters. This will help to choose the right geometric and damping values for pendulum type tilting child seat. The results of the numerical simulations show that the tilting principle can be applied for designing comfortable children travel seats. This is expected to reduce the incidence of nausea as a result of motion sickness. Thus vehicles travel speeds can be increased without a serious decrease of the ride comfort. ACKNOWLEDGMENTS This work was supported by the National Science Fund of the Ministry of Education and Science of the Republic of Bulgaria [Grant No. ДМ 07/8 (December 17, 2016)]. REFERENCES [1] Hannah, J. and Hillier, M. J. Applied mechanics, 3rd Edition. Longman Pub Group, 1996, pp. 464. [2] Persson, R., Goodall, R. M. and Sasaki, K. Carbody tilting – technologies and benefits. Vehicle System Dynamics, 47(8), 2009, pp. 949-981. [3] Hibbard, R. and Karnopp, D. Twenty first century transportation system solutions – a new type of small, relatively tall and narrow active tilting commuter vehicle. Vehicle System Dynamics, 25(5), 1996, pp. 321-347. [4] Mauer, M., Gerdes, J. C., Lenz, B. and Winner, H. Autonomous driving. Berlin: Springer, 2016, pp. 706. [5] Erdman, W. S. Geometry and inertia of the human body - review of research. Acta of Bioengineering and Biomechanics, 1, 1999, pp. 23-35. [6] http://www.actabio.pwr.wroc.pl/Vol1No1/3.pdf [7] Pavlov, N. and Sokolov, E. Tilting child safety seat for reducing the lateral acceleration acting on children when vehicle cornering. Proceedings of the 8th ECCOMAS Thematic Conference on Multibody Dynamics, MBD, Prague, 2017, pp. 779-783. [8] Pavlov, N., Sokolov, E., Peychev, M. and Dacova, D. Design and test of a tilting seat for improving children’s comfort during traveling. Proceedings of the 2nd International Scientific Conference on IT, Tourism, Economics, Management and Agriculture, ITEMA, Graz, 2018, to be published. [9] Miletiev, R., Kapanakov, P., Iontchev, E. and Yordanov, R. Hardware implementation of integrated navigation and inertial system. Proceedings of the International Spring Seminar on Electronics Technology, Sofia, 2017, pp. 623-626. [10] Iontchev, E., Kenov, R., Miletiev, R., Simeonov, I. and Isaev, Y. Hardware implementation of quad microelectromechanical sensor structure for inertial systems. Proceedings of the 37th International Spring Seminar on Electronics Technology, ISSE, Dresden, 2014, pp. 417-420. http://www.iaeme.com/IJMET/index.asp 177 [email protected]