## Possibility of using Simulink in the dynamics of lifting equipment

**Jozef Filas**^{1,}, **Peter Čarnoký**^{1}

^{1}Faculty of Mechanical Engineering, Department of Applied Mechanics and Mechatronics, Technical University of Košice, Letná 9, Košice, Slovak Republic

2. Formulation of Dynamic Motion Equation Mechanical System

### Abstract

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),
pp 394-397.

DOI: 10.12691/ajme-1-7-48

Received October 17, 2013; Revised October 24, 2013; Accepted November 24, 2013

**Copyright**© 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.

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### 1. Introduction

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.

The mechanical system is illustrated on Figure 1 and Figure 2.

**Figure 1**. Overall layout of the lift mechanism

**Figure 2**. Top view of the lift mechanism

Figure 1 and Figure 2 shows the used labeling:

- 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

(1) |

where: *E**k*, *E**red* – are kinetic energies in original and reduced system; *A*, *A**red* – are works of active forces in original and reduced system; *P*, *P**red* – 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

**Figure 3**. Labeling of angular velocities and velocities

Kinetic energy of mechanical system is determined by:

(2) |

If the kinetic energy is expressed in function of angular velocity of the motor *(**ω*_{MOT}), 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:

(3) |

**2.2. Calculation of Work of Active Forses and Moments**

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* φ*_{MO}_{T}.

(4) |

After substituting and expressing gear ratios the work of active forces and moments is:

(5) |

**2.3. Dynamic Motion Equation**

Dynamic motion equation of reduced system is expressed:

Dynamic motion equation of reduced system is expressed:

(6) |

after substitution from equations (1):

(7) |

After substituting (3) and (5) into (6) the final dynamic motion equation of mechanical system is:

(8) |

### 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:

**Figure 4**. The block diagram in Simulink for solving and rendering selected variables

Parameters of variables are saved to the Workspace Figure 5:

**Figure 5**. Workspace with variables data

**Figure 6**. Angular acceleration

Program in Matlab for graphic representation the results from Workspace is in the form:

Simulation results in Simulink from Scope block is in the Figure 7 and Figure 8.

The selected variables are angular velocity Figure 7 and angular displacement of motor Figure 8 of the mechanical system Figure 2.

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.

**Figure 7**. Angular velocity

**Figure 8**. Angular displacement

**Figure 9**. Setting parameters in block Scope

### 4. Conclusion

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.

### Acknowledgement

The work has been accomplished under the research project VEGA 1/1205/12 Numerical modeling of mechatronic systems.

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