drawoh,
Trying to do a motor acceleration analysis while connected to pd pump. This requires the WR2 values for the motor and pd pump. I have the WR2 of the motor. Manufacturer of the triplex pd pump does not have information on the pump's WR2. Can you believe that?
I have the pump HP and Speed. I need to know the moment of inertia (WR2) of the pump. I found a formula to calculate the WR2 of a centrifugal pump, but not for a pd pump. Can you help.
"Positive displacement" pump does not tell us anything. Moment of Inertia is valid only if everything rotates. Piston pumps for example, are positive displacement.
You need to know how the pump works. You need to know the mass of all the components that do linear movement. You need to know the moments of inertia of the rotating components. You need to know how fast they rotate with respect to the drive shaft. You need to know the density of fluid being pumped.
If you know all of that, you should be able to work out the input torque required to accelerate your system, as opposed to moment of inertia.
Can you take a pump and test it with a torque wrench? I cannot see a manufacturer providing the information you need to do any sort of accurate calculation.
Or, attach a pendulum to the input shaft, and measure the period of oscillation at small angles. Then measure the period of the pendulum alone. The change in period is due to the inertia of the pump. Calculations/formulas should be in your 1st year physics text.
"Trying to do a motor acceleration analysis while connected to pd pump. This requires the WR2 values for the motor and pd pump. "
In the real world, the fluid being pumped will have its own inertia, which will come into play as well.
My first answer is to buy a pump with all the specifications you need but since there are few truly good mechanical engineers that can design things instead if evolve or kludge them, getting specifications will be difficult.
I am a control person. The technique you want to use is called system identification. Basically you must write a differential equation or two that models the pump. There are coefficients that you don't know for the inertia and friction. Hopefully you have a model for the motor or you will need to model the motor by itself first. Then as suggested above one accelerates the pump. The torque doesn't need to be constant in fact it is best if it isn't. If the torque is ramped up and down that is better. During this process the torque and angle or torque and velocity is recorded as a function of time. You may be able to get by with sampling every 10 ms but the faster the better. Next an optimizing(minimizing) algorithm is used to figure out the coefficients for the angular acceleration term ( inertia ) and the angular velocity term ( friction ). The Levenberg-Marquardt or BFGS algorithm are algorithms that use trial and error that try different coefficients until the model's estimated velocity as a function of record torque closely matches the actual velocity as a function of torque. Although these methods use trial and error they are designed to converge on the coefficients that minimize the sum of square errors quickly.
There is no easy way to do this unless one has previously written software to do it. I use these techniques to auto tune the PIDs and feed forwards for hydraulic and electric mechanical systems.
I have yet to see a mechanical system that has a transfer function stamped on it. I always must figure things out empirically.
Companies like Caterpillar do this kind of system identification all the time. By the time they are done testing they know more about the product they are testing than the manufacturer.
"How do you account for the friction in the pump?"
It would show up as a decay rate in the oscillation, but won't directly affect the system frequency/period. So, short answer is I wouldn't. Unless you are talking about fluid friction (I was assuming one could use an empty pump).
