Simcenter Amesim Galton Board – Order in Apparent Chaos

Summary

Simcenter Amesim model of a Galton Board to explain how the normal balls distribution can be evaluated using a Monte Carlo study.

Details

Attachments:

Galton_board.ame (2 MB)

The Galton board consists of a vertical board with interleaved rows of pegs. Balls are dropped from the top and bounce either left or right as they hit the pegs. Eventually they are collected into bins at the bottom, where the height of ball columns accumulated in the bins approximate a bell curve (normal distribution).
 

To simplify the model, we will create a 2D Mechanical Simcenter Amesim model and simulate each ball hitting the pegs individually. Then, we will run a Monte Carlo study to analyze the statistically distribution of the different runs with different boundary conditions.  The different boundary conditions dropping the balls are defined through random signals, which provides a small variation on the rotation torque and the forces in the longitudinal and vertical directions at the beginning of the simulation.
 

Here 2 examples of different paths, that the ball can follow depending on the different initial boundary conditions:

Run 1:

Run 2:


Here the trajectory results  of  6 runs with different initial random boundary conditions displayed as a X-Y plot:

Running a Monte Carlo study with 100 different boundary conditions, we can see that the results follow the bell curve (normal distribution) as shown in the statistical theory:



Attached to this Knowledge Base Article you can find the Simcenter Amesim model.