Is there an Optimal RPM for a DC generator?

[superkaho]

Is there an Optimal RPM for a DC generator??

I would like to ask if there is an optimal rpm for a DC generators? Or the faster it rotates, the more power it generates?

The specification of the motor is as follow:
http://www.mitsumi.co.jp/latest/Catalog/pdf/motorav_m25e_11.pdf

 

[Fish4Fun]

The short answer to your question: The faster the motor turns the more power it will produce. At some point in the RPM to Power Curve the coil resistance will become the dominant current limit. The particular motor you referenced shows 2650RPM @ 2.5V and 30mA input, and a maximum current of ~175mA stalled. If you wanted to achieve say 100mA @ 2.5V, I would suggest you start ~10,000RPM. This is an off-the-cuff guesstimate, but looking @ the Current to Torque to RPM graph:

0 Torque @ 2.5V & 30mA = 2650RPM
100mN&M @ 2.5V & ~140mA = ~750RPM

2650/(750/2650) = 2650^2/750 = 9363RPM This is BY NO MEANS an exact calculation; it is just a very rough first level approximation. It would be far easier to simply test the motor rather than attempt to calculate the performance curve based on the rather sketchy figures given. My initial guess of 10,000RPM was based soley on experience with DC motors used as generators; my ad-hoc formula using the data sheet just happened to agree so closely with my guess that I thought i would include it, but I have NEVER attempted to verify if this ad-hoc formula has any validity, likely it does NOT.

Fish

 

[Phrak]

"Is there an Optimal RPM for a DC generator??"

Yes! What do you want to optimize?

 

[superkaho]

"Is there an Optimal RPM for a DC generator??"

Yes! What do you want to optimize?

The motor is used to produce a mini wind turbine.
In order to design it, I have to choose my gear ratio for the motor so as to maximize the power generated. My teacher said that he will measure the average power produced through a load with a 50ohm resistor.

 

[Fish4Fun]

The motor is used to produce a mini wind turbine.
In order to design it, I have to choose my gear ratio for the motor so as to maximize the power generated. My teacher said that he will measure the average power produced through a load with a 50ohm resistor.

Ahhh, ok, now we are getting somewhere! I assume the turbine will be powered by a fan, and that there are restrictions on the blade design? I would suggest that you focus on blade design and eliminate gearing.

The first step is determining the wind speed at the distance from the fan the turbine will be placed. Everything else is dependent on that. Why? The power in the wind is defined as:

P = 1/2 * (Air Density) * (Swept Area) * (Wind Speed)^3 * CP

You already have a good idea what the motor's maximum power consumption is from the data sheet graph: 150mA * 2.5V = 375mW. Next we solve for the swept area required to achieve .375mW for your wind speed, let's call it 15mph (6.7m/s) and use CP = 0.3 as an example:

.375 = 1/2 * 1.23kg/m^2 * A * 6.7^3 * .3 => A = .06758m^2

.06758 = Pi * R^2 => 0.0464m => 1.82in Radius (3.65in Diameter).

This gives us the MINIMUM diameter for your blades to produce 375mW in 15mph winds, but this is only part of the story!

Next we need to calculate the RPM of the blades. I suspect we want to achieve as close to 10,000 RPM as possible. RPM is related to Wind Speed by something called Tip to Speed Ratio (TSR). Typical values for TSR in wind turbines range from 4 to 12. TSR is the ratio of tip speed to wind speed, and in general help describe the airfoil required. Let's see what TSR we would need for our theoretical turbine.

2 * Pi * 1.82in = 11.473in/Rev => 11.473 * (1ft/12in) * (1mi/5280ft) = 1.81 * 10^-4 Miles/Rev => 5522 Rev/Mile

(15 Miles/Hour) * (1 Hour/60 Min) = 1/4 Mile/Min

1/4 Mile / Min * 5522 Rev/Mile * TSR = 10,000RPM

TSR = 10,000/(1/4 * 5522) => 7.24

This demonstrates that a turbine with a 3.65in Diameter SHOULD be capable of turning @ ~10,000 RPM in a 15MPH wind with enough torque to produce .375W if we can achieve a CP of 0.30.

In the design process I would continue to refine the blade diameter/TSR/Airfoil until the maximum power were achieved at the Fan's wind speed.

Fish

 

[Phrak]

You need to provide us your constrains. Are you given a generator you must use, or are you allowed to select your own? Is everything constrained in advance except the gear ratio? What can you vary and what is constrained?

 

[superkaho]

You need to provide us your constrains. Are you given a generator you must use, or are you allowed to select your own? Is everything constrained in advance except the gear ratio? What can you vary and what is constrained?

yes, I must use the given generator to produce the maximum power output across a 50ohm resistor...Suppose the wind speed is 3.5m/s from a fan. What I can vary is the gear ratio, blade shape/material/size (swapped area).

 

[Phrak]

OK. Then a bunch of constraints that you need to communicate are about the air flow and how it is delivered, how much of the mass airflow you can use, or is available, and the generator parameters as if the generator is used as a DC motor.

What kind of generator is it? Does it have field windings (series or parallel), or perm magnets.

What are the generator parameters?
These are the K factors: volts per rpm and and current per unit torque.
Measurable are stall torque, locked rotor current, unloaded current, and DC resistance.