Converting Manufacturers' Hydraulic Pump Data to a Pump Curve and Matching to an Application

The problem: when you select a hydraulic gear pump, the manufacturer's curves are for a certain viscosity and rpm which in general do not match your design.

Worse, if you are driving your gear pump with a permanent magnet DC (PMDC) motor, then the rpm will decrease with load and your actual performance curve will look nothing like the manufacturer's curves. The purpose of this article is to show you how to make those adjustments. I have used this technique in practice and found that it agrees surprisingly well with pump test loop experiments.

Note that the above curve spans a range of rpm's and pressures. This particular curve is from the Marzocchi pump company and is for a viscoity of 30 cSt. In practice, you will need to rework this information to construct a single pump curve where flow rate is graphed against pressure. Note that the above data does not go all the way down to zero pressure, however a flow vs. pressure curve for a properly designed and purposed gear pump is a perfectly straight line. This article will walk you through the steps required to generate your actual pump curve.

Breaking down the data into viscous friction vs. leakage

The observed flow rate vs. pressure depends on two things: viscous friction and leakage. Happily, gear pumps tend to operate at low-Reynolds numbers which makes analysis easy by using laminar flow equations. Our goal here will be to understand the friction and leakage equations only well enough to identify and quantify the contributions of factors we have control over. The most critical aspect of gear pump design, the determination of running clearances, is beyond the scope of this article but will be considered on this Blog in a future article.

Viscous Friction

Let's start with viscous friction. At zero pressure, the pump is doing no useful work, and all of the torque is used to combat viscous friction. Consider the definition of viscous shear. For a plate of area A moving with respect to a fixed surface separated by a gap t:

Clearly the friction torque is the sum of the contributions of viscous shear force elements acting on moment arms across the wetted rotating surfaces of the pump (i.e. you integrate). Right away, the zero-load torque can be adjusted from the manufacturer's value simply by a linear adjustment of the viscosity. Since the friction torque also depends linearly on speed, i.e. rpm, then the friction torque can likewise be easily adjusted for varying rpm also with a simple linear ratio.

Notice that we have not had to consider the actual internal geometry of the pump, which does not change as the viscosity and rpm vary: by giving us the no-load motor torque at a stated rpm and viscosity, the manufacturer has in effect done this for us.

A test against zero pressure tells us:

• The pump displacement
• The friction torque

Internal leakage

Next, the internal leakage needs to be considered. Moving parts require running clearances and these become fluid leakage paths from high to low pressure. As we did for fluid friction, we're going to idealize these leakage paths as simple rectangular gaps, which can in principle be integrated to obtain one overall "fluid resistance", analogous to electrical resistance, for the entire pump.

Again, by giving us the pump curves, the manufacturer has provided enough info to deconstruct this data and solve for the leakage at various pressures. So we will use the published flow data to determine the volumetric efficiency of the pump and thus the "resistance" term on the right of the above equation.

Volumetric efficiency

In other words, by giving us the actual flow rate at two rpm's, the manufacturer has given us the data we need to calculate volumetric efficiency. Since we know that the leakage flow rate at zero pressure must be zero, and thus volumetric efficiency is 100%, we can easily calculate both the pumps' leakage flow resistance (above) and also the pump displacement.

At non-zero pressure, you cannot directly measure viscous friction (counting journal bearing friction). However, if you know the rpm and the actual flow rate, you can calculate the volumetric efficiency and thus infer the viscous friction and seal friction losses.

Practical simplifying assumptions

We are going to make an assumption here that experiment shows holds up well in practice: assume that the leakage resistance depends only on the terms in the above equation, in particular those terms we have control over: the viscosity and the rpm. In theory, pump leakage resistance due to viscous shear depends on the speed of the fluid with respect to the surfaces of the leakage gap, and those surfaces are not stationary (the gear surfaces rotate), meaning that the actual leakage flow speed will depend on the magnitude of the vector sum of the leakage and moving surface speeds of the parts, and that the leakage flow down the journal bearing shafts is similarly complicated by both the surface speed and a changing eccentric gap. However, it can be shown experimentally that these effect can be ignored. 

Once the fluid resistance term above has been determined for your pump, this number can easily be adjusted for a different viscosity. Again, we assume that fluid leakage will vary from this term only due to changes in viscosity.

But be careful: volumetric efficiency depends on both leakage and pump output: the displacement and the rpm. At any pressure, the faster the rotation speed, the greater the volumetric efficiency. Changing the rpm's will dramatically effect the pump flow rate at pressures near pump stall.