Possibility of using Simulink in the dynamics of lifting equipment
1Faculty of Mechanical Engineering, Department of Applied Mechanics and Mechatronics, Technical University of Košice, Letná 9, Košice, Slovak Republic
The topic of solving lifting equipment includes, among other things, the solution of motion dynamics of mechanical system with regard to the relationship between drive of the system and selected kinematic variables. This article demonstrated the possibility of using MATLAB-SIMULINK and the method of weight and force variables reduction. In a similar manner it is possible to apply for different system configurations mechanical lift machine.
At a glance: Figures
Keywords: motion dynamics, lifting equipment, method of weight and force variables reduction
American Journal of Mechanical Engineering, 2013 1 (7),
Received October 17, 2013; Revised October 24, 2013; Accepted November 24, 2013Copyright © 2013 Science and Education Publishing. All Rights Reserved.
Cite this article:
- Filas, Jozef, and Peter Čarnoký. "Possibility of using Simulink in the dynamics of lifting equipment." American Journal of Mechanical Engineering 1.7 (2013): 394-397.
- Filas, J. , & Čarnoký, P. (2013). Possibility of using Simulink in the dynamics of lifting equipment. American Journal of Mechanical Engineering, 1(7), 394-397.
- Filas, Jozef, and Peter Čarnoký. "Possibility of using Simulink in the dynamics of lifting equipment." American Journal of Mechanical Engineering 1, no. 7 (2013): 394-397.
|Import into BibTeX||Import into EndNote||Import into RefMan||Import into RefWorks|
mple a passenger lift, requires knowledge in fields of electrotechnics, hydraulics, flexibility and hardness, but also of kinematics and dynamics.
In this article we show the possibility of using the programming environment MATLAB-SIMULINK to find relationships between selected kinematic variables and the drive in motion of a particular passenger lift.
We will use a passenger lift with capacity of 500 kg, transport velocity of 1.2m/s, controlled by microprocessor, with rope electric drive.
- MOT - motor;
- SP - clutch;
- BR – brake;
- OK1....OK4 – cogwheels 1....4;
- BUB – drum;
- L – rope;
- KL – pulley;
- KAB – car;
- PRZ – counterweight;
- H1....H7 – shafts 1....7.
2. Formulation of Dynamic Motion Equation Mechanical System
Mechanical system of a passenger lift represents a mechanism with one degree of freedom.
To compile the dynamic motion equation of this mechanism we use the method of weight and force variables reduction.
To ensure a dynamic equilibrium of original and reduced system, conditions have to be met
where: Ek, Ered – are kinetic energies in original and reduced system; A, Ared – are works of active forces in original and reduced system; P, Pred – are powers of active forces and moments in original and reduced system.
Motion of original system is reduced to motion of motor.2.1. Calculation of Kinetic Energy of the System
Total kinetic energy of mechanical system is the sum of kinetic energies of its individual members, depending on the motion, which they perform. Figure 3 shows the diagram in terms of angular velocities about axes of rotation and members that perform translational motion
Kinetic energy of mechanical system is determined by:
If the kinetic energy is expressed in function of angular velocity of the motor (ωMOT), after quantification of the masses of individual members of the system and their moments of inertia (members that perform rotational motion), then the kinetic energy of the original system is:
We determine the work of all active forces and moments that act on the individual members of the system (see Figure 3).
The work is expressed in a function of motion of selected system member, in this case the function of motion of the motor, thus its rotation φMOT.
After substituting and expressing gear ratios the work of active forces and moments is:
Dynamic motion equation of reduced system is expressed:
Dynamic motion equation of reduced system is expressed:
after substitution from equations (1):
After substituting (3) and (5) into (6) the final dynamic motion equation of mechanical system is:
3. Results of the Solution Using Matlab-Simulink
Solution of differential equation (7) the mechanical system is performed using Simulink blocks. The scheme for solving equation (7) in Matlab/Simulink is in the Figure 4:
Parameters of variables are saved to the Workspace Figure 5:
Program in Matlab for graphic representation the results from Workspace is in the form:
Starting time is limited by time during which the lift car reaches traveling speed.
The shape of the curve of input torque of motor is in fact different from constant. Its course is part of the documentation to the supplying of motor and it is a commercial matt.
Results of the solution can be verified by another method. Simulation motion are given as an example, for each specific type of lift is to be expected with the technical data.
The work has been accomplished under the research project VEGA 1/1205/12 Numerical modeling of mechatronic systems.
|||Beer Ferdinand P., - Johnston Russel E. (1988), Vector mechanics for engineers. 5th ed, New York: McGraw-Hill.|
|||Bocko J., Filas J., Huňady R., Sivák P. (2011),Dynamika v príkladoch, Košice: Technická univerzita v Košiciach, Strojnícka fakulta.|
|||Budó von A. (1987), Theoretische Mechanik, Berlín: Dt. Verl. der Wissenschaften.|
|||Čarnoký P. (2011), Dynamická analýza pohonnej sústavyzdvíhacieho mechanizmu s využitím Lagrangeových rovníc II. druhu - Bakalárska práca, Košice.|
|||Filas J., Čarnoký P. (2011), Personal elevator and its drive In: Modelling of mechanical and mechatronical systems. Proceedings of the 4th international conference, Košice: Sjf TU.|
|||Hořejší J. (1980), Dynamika, Bratislava: Alfa.|
|||Janovský L., Doležal J. (1980), Výtahy a eskalátory, Praha: SNTL.|
|||Janovský L. (1991), Systémy a strojní zařízeňí pro vertikální dopravu, Praha: ČVUT.|
|||Janovský L. (1971), Výtahy a eskalátory I, Praha: ČVUT.|
|||Kaczorek T., Marchenko V., Sajewski L. (2008), Solvability of 2D hybrid linear systems - comparison of three different methods, Acta Mechanica et Automatica, Vol. 2, No. 2., pp. 59-66.|
|||Lukáč Z., Elischer J. (2002), Technická správa, Košice.|
|||Medvec A., Stradiot J., Záhorec O., Caban S. (1988), Mechanika III, Bratislava: Alfa.|
|||Meriam J.L. (1978), Engineering mechanics, New York: Wiley.|
|||Stradiot J., Michalíček M., Mudrik J., Slavkovský J., Záhorec O., Žiaran S. (1991), Dynamika strojov, Bratislava: Alfa.|
|||Trebuňa F., Šimčák F. (2005), Pružnosť, pevnosť a plastickosť v strojárstve, Košice: EMILENA.|
|||Záhorec O., Caban S. (2002), Dynamika, Košice: Olymp s.r.o.|
|||Záhorec O., Michalíček M., Žiaran S. (1991), Dynamika: zbierka príkladov, Bratislava: Alfa.|