Drive dynamicsof passenger liftin Simulink

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Figure 2. Lift motor

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Figure 3. Brake

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Figure 4. Transmission

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Figure 5. Sprocket

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Figure 6. Transmission shaft with flange

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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:

(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

(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

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Tables index

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Figure 7. Selected kinematic parameters

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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

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Then generalized force will be

(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

(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

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

Figure 10. Block diagram of the mechanism

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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

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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

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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

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