Peristaltic pump head torque calculation

[Chanveer Patil]

If I know that a 0.5 mL/min max flow rate and tube size of 0.5 mm ID x 2.5 mm OD, pump head 6 rollers of 12 mm and 44 mm head dia. how do I calculate torque generated by pump head to a selection of motor for peristaltic pump.
Any suggestions of places to look for calculations, or resources for learning more? I'm a mechanical engineer, but not a pump designer by any stretch of the imagination, so I may be a bit dense and overlooking something obvious.

Thanks in advance for any help or suggestions the forum may have!

:-Chanveer Patil

 

[Compositepro]

Torque is required to deform the tubing and to push the liquid against a back pressure. If the tubing were perfectly elastic the energy required to squeeze the tubing would be recovered when un-squeezing it. Energy is lost in the hysteresis of the tubing material. Creating flow with no pressure takes little energy to simply accelerate the fluid from zero velocity (entrance losses at the beginning of the tube). Treat the pump like a piston pump. Cross-sectional area of the tube ID times the velocity times the pressure gives the power requirement. You may find the biggest factor is the hysteresis (basically friction).

 

[3DDave]

It's even easier as the flow rate is given, so multiply the 0.5mL/min times the deltaP to get the energy required to produce that flow. Still, at that flow rate and diameter, hysteresis in the tubing and friction in the roller bearings will likely overwhelm the power required to produce the flow. These are going to need to be experimentally determined, but you set up a test with one roller and the tubing. Put a load on the roller sufficient to pinch off the tube and then see how much force is required to cause it to roll along the tubing. Maybe an afternoon to set up and get a fish weighing scale to measure the drag.