Fixed-displacement pump friction torque vs pressure gain coefficient

I had fixed-displacement pumps in my model in 2016a. When I transfered to 2016b, the old fixed-displacement pumps automatically updated to the new ones. One parameter that puzzles me is the friction torque vs pressure gain coefficient. For me it has taken efficiency parameters from the previous version blocks and is now calculated as:

1.5915e-07*(pump_displacement)*((volumetric_efficieny)/(total_efficiency)-1) [Nm/Pa]

What is the logic behind this? I can't find anything in the documentation. The pump displacement is in cm^3/rev, which might affect the first constant but there must be some other factors as just converting from cm^3/rev to m^3/rad does not result in Nm/pa.

[Michelle Wu]

I have been sorting through the documentation but I was not able to find the equation you posted. Can I ask where did you get this equation? Is it a guess based on your experiments/simulation or is it documented somewhere?

cm^3/rev and m^3/rad are both units for pump displacement. The unit out of the equation you posted should also represent pump displacement. From my perspective, the "friction torque vs pressure gain coefficient" should just be an input parameter defined by the user. It is the proportionality constant between the friction torque and pressure gain, and thus the unit is in N*m/Pa.

[Tom]

This equation is not in the documentation. Simulink just decided to use it when I opened my old 2016a model in 2016b. The unit out of this equation should indeed be pump displacement as the efficiencies are unitless. This would mean that the 1.5915e-07 constant has some hidden unit conversions. I would just like to know what this conversion is based on for the sake of personal documentation. I'll attach an image of my pump block.

Answer 1

[David Goodmanson]

Hi Tom, If you convert units from cm^3/rev to m^3/rad, then the value itself picks up a factor of 1e-6/(2*pi) = 1.5915e-07, and the units on either side are m^3 and Nm/Pa = N*m/(N/m^2) so this appears to be correct.