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Drive dynamicsof passenger liftin Simulink

Jozef Filas*, Milan Andráši

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

Abstract: This article deals with the compilation of dynamic motion equations of freight lift mechanical system with the aim of simulating its dynamics in programming environment Simulink. Calculations in Simulink can be done for different values of acceleration when starting the lift. Orstart-up behavior for different engines. Similarly, you can do the same for the case of deceleration (stopping) code to the elevator

Keywords: dynamic motion equations, mechanical system, simulation

Received October 04, 2013; Revised October 14, 2013; Accepted November 13, 2013

Citation: Jozef Filas, Milan Andráši, Drive dynamicsof passenger liftin Simulink. American Journal of Mechanical Engineering, 1 (7). 361-364. January 2013. doi:10.12691/ajme-1-7-41

1. Introduction

The issue of passenger lift drive solution is extensive and reaches many aspects.

This covers the requirements of the mechanical parts of the drive system but also the requirements in terms of drive control.

A very important requirement derives from subjective feelings of the lifts users. The point is that the different phases of motion of passenger lift, such as start, steady running and stopping, are the most enjoyable for passengers or acceptable for cargo.

Programs of motion control of lifts are initially based on the analysis of motion of mechanical system of lift mechanism. This paper describes the creation of a mechanical model of the mechanical system and the simulation of its motion in programming environment SIMULINK.

2. Parts of the Freight Lift

Figure 1 shows overall system configuration of freight lift mechanism:

K is cabin,

Z counterweight,

E electromotor,

1 brake,

2, 3 transmission parts,

6, 7 clutch,

8, 9 transmission shafts,

14, 15 chains,

10, 11, 12, 13 pulleys

4, 5 sprockets.

Basic technical parameters of the lift:

- load capacity 500 kg, cabin of mass 550 kg,

- velocity 0,18 ms 1 ,

- drive, electrical power of motor 1,8 kW, RPM 960 rates min⁻¹

Figure 2 through Figure 6 show photos of selected mechanism parts of the lift drive.

Figure 1. Schema of the lift mechanism

Figure 2. Lift motor

Figure 3. Brake

Figure 4. Transmission

Figure 5. Sprocket

Figure 6. Transmission shaft with flange

3. Dynamic Motion Equation of the Mechanism

Lift machine presents a mechanism with one degree of freedom.

To compile dynamic motion equations of this mechanism we will use Lagrange equation of II. kind in form:

[picture] | (1)

where: Kinetic energy of system,

Generalized coordinate,

Generalized velocity.

3.1. Calculation of Kinetic Energy of the System

Kinetic energy of total mechanical system is determined

[picture] | (2)

Kinetic parameters of individual system members (velocities or angular velocities) are determined in velocity function of the lift cabin.

Schema with labeled kinetic parameters is illustrated on Figure 7.

Table 1. contains calculated and measured values of masses, sizes, moments of inertia and kinetic energies of individual members of mechanical system.

Table 1. Partial results

Figure 7. Selected kinematic parameters

3.2. Calculation of Generalized Force

Figure 8. indicates virtual displacements and virtual rotation of members of the mechanism.

These will be expressed in function of virtual displacement of the cabin.

Figure 8. Virtualmovements

Then generalized force will be

[picture] | (3)

3.3. Lagrange Equations of II. Kind

After substitution to (1) for kinetic energy and corresponding derivations, for generalized force we get dynamic motion equation of the mechanical system (using L. equation of II. kind) in form

[picture] | (4)

For the purposes of simulation we consider passive resistances in the system of size of 20% of the nominal torque of motor.

4. Motion Simulation in SIMULINK

Schema of the lift mechanism Figure 1. is for the use of SIMULINK simplified into form shown on Figure 9.

Figure 9. Modified schema of the mechanism

Figure 10. shows block diagram of model of the mechanism.

Figure 10. Block diagram of the mechanism

4.1. Simulation

Using parameters of specific mechanical system of a freight lift we simulate motion i.e. relationship between velocity and acceleration of the cabin depending on torque of motor.

Figure 11 shows relationship between cabin velocity () and time () it takes to reach travel velocity, if highest velocity is reached time of .

Figure 11. Relationship speed cab-time

Figure 12. shows relationship between cabin velocity and time, but with modified (smoother) start of cabin. Smallest time it takes to reach travel velocity is .

Figure 12. Adjustedstarta lift

Figure 13. shows graph of cabin velocity increase with even smoother start than in Figure 11.

Demands for prescribing size of acceleration during start depend on transported wares or persons (more sensitive or conventional materials etc.).

Figure 13. Simplified start of cage

This way we can simulate motion dynamics of mechanical system of a lift for various cabin acceleration sizes depending on trasportation requirements.

5. Conclusion

Similar manner it is possible to simulate the elevator start acceleration for different sizes and for various forms of learning curves.

Acknowledgement

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

References

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