TPT September 2017

AR T I C L E

Advanced Machine & Engineering/AMSAW

The torsional natural frequencies and mode shapes are:

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.

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

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).

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.

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SEPTEMBER 2017