In the US, a mil is a thousandth of an inch and for rotating equipment vib refers to the displacement usually expressed as a pk/pk value.
IPS is vibration usually expressed in the US as pk/0 value.
If displacement is sinusoidal x(t)=X0*sin(w*t)
then velocity will be
v(t)=d/dt (x(t))= w*X0*cos(w*t).
Hence the conversion between mils and ips is frequency-depdendent.
The conversion I use to convert between displacement magnitude in mils pk/pk (X) and velocity magnitude in ips pk/0 (V) assuming single frequency sinusoid at frequency F (cpm) is follows:
X = V * (18,000/F)
V = X * (F/18,000)
Those are round numbers... it's actually closer to 19,000 but 18,000 is a good round number when you are converting to speeds like 3600, 1800, 1200 etc.
You can verify the result for yourself using first principles v(t)=d/dt (x(t))= w*X0*cos(w*t) taking using suitable unit conversions and the fact that V is expressed as PK/0 while X is expressed as PK/PK (in the US).
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