Dear Keith,
Frequency depends on phase between the action of forces. In practical terms,
the amplitude and frequency of vibration it depends on
Spring constant of connection
Mass of wagon
Damping factor
Number of vibrating elements
Slack in connection
In the case of the rail system the vibration can also be driven by a forced
vibration from the wheels and track in ways that are speed dependent
The theory is of tuned mass-spring-damper systems. If they oscillate, they
are an under-damped system
Such systems oscillate at natural frequencies you can determine
mathematically (though sometimes the maths is tough manually, it is easy on
many calculators and with software such as MathCAD). To save me trying to
write the theory on a text only list email, Here is the intro for a single
wagon element that deals with the problem without the slack (adding slack to
the coupling adds a lot of speed and acceleration-related complexity)
http://www.seas.upenn.edu/~ese112/labs/MSDSystemLecturePart%202.pdf
In the case of a train composed of multiple wagons the solution is by
linking a lot of the above together. Mathematically its easiest to solve it
by matrices to find the eigenvalues and eigenvectors.
There's a good description here
http://wapedia.mobi/en/Vibration?t=1.
The second page has the start of an explanation on multiple wagon designs
(see multiple degree of freedom).
The standard method of removing the vibration effect is to change the
mechanical properties of the system to move the frequency of the vibration
to a speed range where it doesn't matter. The problem with rail systems is
the available changes tend to move the shake rattle and roll to when the
train is at normal travelling speed which presents many more significant
problems particularly of safety - much better to have the oscillations at
low speed when the train is just starting up.
BTW, The Saab 9-5 is a car that the designers appear to have got badly wrong
in exactly this respect. They increased the softness of lining elements in
the suspension to decouple vibration and the result on models a few years
old is at speed the wheels shake in a steady vibration at the drop of a hat.
Best,
Terry
-----Original Message-----
From: PhD-Design - This list is for discussion of PhD studies and related
research in Design [mailto:[log in to unmask]] On Behalf Of Keith
Russell
Sent: Thursday, 19 November 2009 9:43 AM
To: [log in to unmask]
Subject: Re: concatenation - trains and shunting
Dear terry
thanks heaps for this excellent account - I've got the first half of my
answer - now I need to know the forces that determine the speed of the wave
and whether the speed is related to the overall speed of the train or
whether it is generated by the wave?
keith
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