# Calculating the power of a pneumatic piston vibrator

I am using a pneumatically-driven piston vibrator to compact a tank filled with granular material. The intensity of the vibrator can be regulated by changing the pressure of the pressurized air fed into the vibrator (from 2 to 6 bar). The manufacturer specifies the force generated by the vibrator at 2, 4 and 6 bar.

However, we would like to find the total energy delivered into the system during the vibration time. So we are looking to calculate the power (Watt) of the vibrator and multiply it by the vibration time (S), to get energy (J).

The principle of the piston vibrator consists in a piston which is propelled inside a cylindrical housing by pressurized air. A schematic can be seen here:

E - Pressurized air entrance

F - Air exit

Force (at 6 bar) = 1000 N

Frequency (at 6 bar) = 100 Hz

(Source data: /www.aldak.com/pneumatic-vibrators/fp-series.html)

The internal piston is in the topmost position in the picture and it is propelled downwards when air is fed.

What I have come up with until now is to assume a distance covered by the piston inside the housing of 1 cm and:

$$1e^{-2} \mathbf{m} * 1000 \mathbf{N} * 100 \frac{1}{\mathbf{s}} = 1000 \mathbf{W}$$

This seems to be a bit high, and I presume one of the problems is the assumed covered distance, however

Does anyone have any advice or idea how one could better calculate the power of the vibrator?

This is a hard problem. Here is how to establish an upper bound on an estimate of the power delivery:

For any mechanical process in which power is being exchanged between components, the magnitude of the power exchange will always be the product of an effort variable and a flow variable at that point of exchange.

So this means that the power input to the pneumatic motor will be the source pressure times the mass flow rate of air entering the motor (and take care with the units!). If the efficiency of the motor was 100%, then that would be the power input to the load that the motor is driving.

Is the force constant for the entire delivery? It will not necessarily be force multiplied by distance as the work done is the integral of force over the distance. This is something the manufacturer may have an answer to that is not listed on the website. If it is a constant force, your formula of:

Travel X Force X Frequency = Work

should give a reasonable estimate of the work done by the piston but it does not account for the total power input of the system.

• We already questioned the manufacturer, they basically replied that they do not calculate those values and are not interested in doing so – Keine Mar 22 '19 at 9:14
• The force is not constant, as it is a (according to the manufacturer) sinusoidal vibration. You are right, the formula is not as straightforward. It should be easy to create the sinusoidal progression of the force and integrate it – Keine Mar 22 '19 at 9:16
• How do you define your system? Are you looking only for the vibratory power added to the system or are you looking for all energy input? – ZackWoodRD Mar 23 '19 at 14:32