Conversion confusion

[joebar32]

I don't normally deal with vibration measurement but a customer requires us to meet a 60 micro-m total amplitude (peak to peak) maximum on a piece of rotating equipment.

Our measurement equipment is an SPM Instruments VIB-11 that reads vibration as in/sec RMS. The mfg provides a conversion card to convert velocity (in/sec RMS) to displacement (mils) at various rotational speeds (3600, 1800, etc.).

The problem is that my customer is questioning the method of conversion. I'm too rusty and the matter is too urgent (LD's on shipment) for me to relearn the issue in order to convince them what is right.

Does anyone have the math for converting an RMS velocity to Peak-Peak displacement?

 

[alexit]

Assuming the in/sec peak occurs at running speed (usually true) then convert this to RMS amplitude by dividing by running speed and (assuming its a pure sine wave) convert to p-p by dividing by .707 and multiplying by 2. Then convert to micrometers...

Like this:

RMS in/sec * 1/running speed * 2/.707 = p-p (IN INCHES)

 

[joebar32]

Thanks. That's right on track.

I somehow was forgetting the meaning of RMS (.707).

 

[electricpete]

I'm not sure the previous approach is right. Let's asssume a sinusoid as above.

D = D0 * sin(2*Pi*f*t)

v = dD/dt = D*2*Pi*f*cos(2*Pi*f*t)

So even if you are correct in the assumption that f corresponds to running speed, what happened to the 2*Pi?

Here is the formula I remember for converting inches per second rms to mils (0.001") peak to peak. I'm sure it can be derived from v = dD/dt = D*2*Pi*f*cos(2*Pi*f*t) with appropriate consideration of units, rms, pk/pk etc.

D ~ (18000/f) * v
where
D is pk/pk displacement in mils (0.001") and
v is rms velocity in inches per second
f is frequency in cycles per MINUTE. This is the RPM of the machine if vibration is at running speed.

Another thing to clarify with your customer is whether he wants true peak-to-peak of a non-sinusoidal waveform. If this is the case there is no way to convert, you need an instrument which will measure true peak to peak displacement.


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[electricpete]

Here's a test case for any formula you use

If vibration is sinusoidal at 1800 cpm (30hz), 0.1 ips rms corresponds very closely to 1.0 mils peak-to-peak

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[fwcatr]

joebar32,

Some time ago I came across two simple calculation programs on the internet that were free for the downloading. It is a good double check of your calculations type of thing from some reputable companies, plus it could be used to gain a better understanding of what you are asking.

One calculator is from Wilcoxin and can be found at

http://www.wilcoxon.com/knowdesk_calculator.cfm

The other calculator is from DLI Watchman and it can be found at

http://www.dliengineering.com/section.asp?nID=19

along with two other programs.

Also, if you go to the following link,

http://www.bksv.com/2148.asp,

you can download some primers on various subjects with one being "Measuring Vibration."

Regards,
Fred

 

[joebar32]

Thanks all.

I've got it squared away to the customer's satisfaction based on info from the instrument mfg., but this has been very useful to refresh my memory of what is going on.

Fred, I'll be sure to check out those programs. I'm always looking for simple, quick ways to get answers. It's tough being a glorified clerk and forgetting all the stuff I went to school for. Luckily I have home improvement projects that are just ripe for being overengineered (new boiler).