Modeling Of Mechatronic System

Modeling of mechatronic system.

To examine oscillations we are taking one part of „Profibus Dp Lm 9681“ mechatronic transport system. This test rig is taken as analog of real conveyor belt trasnport machine for a cheaper investigation. It is shown in Fig 1.

Our system is constisting of two pulleys J1, J2 and mass m1 between them. So our system location difine three generalized coordinates (pulley 1 angle of rotation , body linear displacement and pulley 2 angle of rotation ). We need to calculate generalized coordinates and mass displacement between pulleys. However these generalized coordinates can be called moments, proportional spring elements rotations.

Here is mass motion equation using second type of Lagrange equation

There is ???? - mass [kg], ???? – stiffnes [N/m], ℎ – damping [Ns/m], G – gain

Here is shown in (Fig. 4) a plot natural frequency of conveyor frame.

We saw from the picture that there is periodically damped oscillations with natural frequency, wich equal: f=1T=10.083=12Hz. When we have periodically damped oscillations amplitude ratio between two waves is constant and doesn’t change all the time. This parameter is one of the most important periodically damped oscillations.

Here is shown in Fig. 5 effected system respons – suporting body natural frequency.

Investigation model meshed, it can see in Fig. 6. And its detail is tiped in Table 1.

Here are presented vibrate mode shapes and natural frequencies (Fig. 7-11). Every structure can vibrate without external force, it is called natural frequency. The lowest frequency of „first“ is called The Fundamental frequency. Higher frequency multiples are called Harmonics. Also each natural frequency is associated with a different shape of the structure, called mode shape. If dynamic load coinciding with a natural frequecy it can cause Resonance. Damping exist in real structure to limit the response.

In this project work presented investigated device and short review about mechanism structure. According with dynamic model creation rules here was made dynamic model of conveyor belt. Identificated main characteristics of the transporter. Written mass motion, kinetic and potention energy equations. According dynamic model here was made simulation with simulink program. Get plot diagram of acting and effected systems parts. Using Solidworks software program made body mesh and five shape modes of natural frequency.

Vytautas Kazimieras Augustaitis 2000. Mechaninių virpesių pagrindai. Lietuva, Vilnius Žiburio leidykla 85-102 p.