TPT September 2017

AR T I C L E

Advanced Machine & Engineering/AMSAW

by Willy Goellner, chairman and founder – Advanced Machine & Engineering/AMSAW

118

SEPTEMBER 2017

The torsional natural frequencies and mode shapes are:

From this diagram one can see where the nodes which are

standing still are and which parts are moving against each

other.

You can also see where torsional dampers will be effective,

and how a flywheel affects the system.

For real-world problems the use of a numerical system such

as Octave with necessary coding is needed to handle the

large matrices efficiently.

One other approach is the use of OpenModelica, which is

quite intuitive to use for developing a gear train.

Basically you drag and drop predefined objects, link them to

represent your system and set the parameters.

Example: Input is a sine-signal with a certain frequency. (See

picture below).

If you mount an accelerometer and measure the angular

acceleration you can see the vibration with its homogeneity

and a particular solution.

Due to damping the system is settled within a certain time

frame as you can see in the following charts.

Afterwards you can measure the amplitude. You can repeat

this for several frequencies.

If you show the amplitude vs frequency you get a chart like

this:

This shows that at around 300 rad/s and 750 rad/s the

amplitude has a peak.

These are the two resonant frequencies.