Simulation and Visualization of Dynamic Systems Project

ETLS 789:

Simulation and Visualization of Dynamic Systems class

University of St. Thomas

Fall Semester 2014

Jaw system movement:

A Cam driven by motor

Instructor: Dr. Michael Hennessey

By: Ahmed Elhadeedy

Introduction

Nowadays we see different kinds of machines with variety of constructions or functions. A rotating cam is one of the most important parts in any machine. Most of the machines already have a rotating cam that moves something or opens and closes some parts of the machine. Tetra Pak machines are based mainly upon the idea of a Cam moving a cutting jaw up and down to cut and form the packages. We will mainly discuss this system as dynamic system which consists of a cam, springs, viscous damping, and 3 types of mass, as the jaw will be treated as a mass. All those parts will be shown in a FBD (Free body diagram) all together to show the whole system, and then every part will be discussed separately to see what the forces that are subjected to every part. Then we will simulate the equations of this system using SIMULINK and then getting the output as a plot and values to use it in SOLIDWORKS where the 3D module is being created and being animated.

How does the Cam look like inside the machine?

This is how the cam really looks like inside the machine. The cam follower is attached to jaw and both of them are moving as one part.

The cam follower is depending over the cam through a ball bearing, and the cam has a lower curve which allows the cam follower to go down and also the jaw.

The cam is being driven by a motor with only two speeds, normal (production speed) and inching (slow speed for maintenance purposes).

Fig 1- Cam type 1 – Tetra Pak tba8

Some other types of cam systems uses tension springs and belts to make sure that the cam follower is always attached to the cam.

Fig2 - Cam type2 – Tetra Pak tba 19

System Analysis

The jaw will be treated as a mass with springs and viscous friction on both sides (Machine body and cam follower side), and Let the jaw be M 1with two damping

forces (spring and viscous friction) between it and the cam follower k 2∧B2 and the same between the jaw and the machine body K1∧B1 with

displacement x1.

The cam follower is considered to be a mass M 2connected to

machine body through a tension spring K5 at the RHS of the system and spring and a viscous damping at the LHS of the

system K4and B4.

The Cam follower is relying on the cam through a ball bearing which being simulated as a damping springK3∧viscous frictionB3.

The Cam is being driven by a motor with a torque of τ aand a frictionf c.

System parts and free body diagrams

Fig3−Forces on M 3 the ball bearing

Fig 4 – Forces on M 2the cam follower

Fig 5 – Forces on M 1the jaw

Fig 6 – Forces on the cam which they are τ aand a frictionf c.

System equations:

M 3 equation: M 3 x3=f c−K3 ( x2−x3 )−B3(v2−v3)

M 2 equation: M 2 x2=−B3 (v2−v3 )+ K2 ( x1−x2 )+K3 ( x2−x3 )−K2 ( x2−x3 )−K4 x2−B4 v2

M 1 equation: M 1 x1=−B2 ( v1−v2 )−K2 ( x1−x2 )+K1 x1+B1 v1+M 1 g

Camequation : J w=τ a - f c

Scenario #1:

Fig 9 shows the assumed steady state when forces on the cam are very low.

Fig 9 – Assumed Steady state condition

Fig 10 – Maximum Force over the cam

%The parameters values in MATLAB to export an excel file to use in the design in SolidWorks :

B1 =7;

B2 =15;

B3 =8;

B4 =11;

Fc =75;

K1 =5.5000;

K2 =6;

M2 =200;

Ta =102;

V2 =3;

V3 =6;

k1 =2.2000;

k2 =2.5000;

k3 =2.3000;

k4 =2.4000;

m1 =150;

m2 =200;

m3 =300;

%To save the values of the plot graph as values to use it SOLIDWORKS as a design table

for c = 1:Index_c

y = simout(:,:,c) %Simulink data

xlswrite('testdata.xls', y)end

SOLIDWORKS 3D system

References:

1- Tetra Pak TBA 8 – TBA 19 maintenance document.