Graphing Rate of Change

[Mika Myers]

I am interested in finding a formula that will graph the rpm of a rotor (along the y axis) as the amount of work being done increases. In this case, the work being done is expressed as an increase in differential pressure along the x axis. I also have the increase in torque as a value.

Any help would be appreciated.

Mika

 

[HallsofIvy]

The "increase in torque" tells you about the force applied to the axle. But how the axle reacts to that force depends on many things you have not mentioned.

 

[Mika Myers]

Rate of Change

My purpose is to define the RPM of a rotor (in a down hole mud motor) as the torque increases (differential pressure and torque in this case are parallel) at a given flow rate. The torque is linear and is expressed as (differential pressure/maximum differential) x maximum torque. The calculated efficiency is the Mechanical HP / Hydraulic HP. The actual efficiency at the given flow rate as the differential pressure increases decreases. I have calculated the Mechanical & Hydraulic HP at the given flow rate, but the "Real Efficiency" isn't accurate. I have attached the graph supplied from the manufacturer with the correct values. Help would be greatly appreciated.

 

[Deleted member 4993]

My purpose is to define the RPM of a rotor (in a down hole mud motor) as the torque increases (differential pressure and torque in this case are parallel) at a given flow rate. The torque is linear and is expressed as (differential pressure/maximum differential) x maximum torque. The calculated efficiency is the Mechanical HP / Hydraulic HP. The actual efficiency at the given flow rate as the differential pressure increases decreases. I have calculated the Mechanical & Hydraulic HP at the given flow rate, but the "Real Efficiency" isn't accurate. I have attached the graph supplied from the manufacturer with the correct values. Help would be greatly appreciated.

View attachment 3107

You need to use:

Power = Torque * angularspeed * (fudge factor)

then

angular speed = Power/Torque * (1/fudgefactor)

Don't forget the conversion factor involved in converting (ft-lb/minute) to HP

 

[Mika Myers]

Not there yet.

Using the formulas you provided, no matter the combination of the fudge factor (even using the same for each formula), the result is linear (unless of course, I screwed up in my calculations). Clearly, the graph of RPM at each given flow rate is not linear. The RPM decreases gradually at first, by the time the max differential line is crossed (750 psi), the RPM decreases at a greater rate.

This is driving me bananas.

Thanks for the help.

Mika

 

[HallsofIvy]

The problem is that the "fudge factor" that Subhotosh Khan refers to is NOT necessarily a constant. It includes all of those "things you have not mentioned" that I referred to before. Without more detailed information about exactly what is going on- the "load" on the rotor, etc.- your "model" is not going to give realistic results.