Power, speed, and torque... AGH

[Gui Cavalcanti]

Alright, so my last big discussion here was linking friction, traction, and torque as applied to drive trains. Here's what I'm confused about now: linking power, speed, and torque together.

Alright, I know the basics. As speed increases, torque decreases, and vice versa. You can use the motor charts to find your speed at a certain torque, you can make a drive train by know the force you want your robot to push with and then porting it through the wheel radius, back through the gearing, to your motor. I've got all that. Now I'm struggling with how power affects FIRST robots.

Power is work over time, I know that. Work is force times distance, I know that. But why do we need this rating? What is power, technically, to FIRST robots?

If I build a pulley system with a motor lifting a 20 some kilogram weight (200 N, for arguments sake), wrapping the rope around a 2 centimeter radius shaft, the torque required for this is 200 Newtons * .02 meters, translating into 4 Newton*meters. I decide that I want my motor to operate at 200 mN*m, so my gear ratio is 4/.2, or 20:1.

Now that I have my gear ratio decided upon and I know how my motor will be acting, I can find the speed. Let's say that, when the motor has a torque of 200 mN*m, it's spinning at 500 rpm. This is transferred through my gear ratio, resulting in 25 rpm in the shaft. 25 rpm, multipled by (1/60) to convert to seconds, and (2*pi*.02 meters) to convert to linear motion, means that the weight is being lifted at around .05 meters/second.

Ok, I know how to do all that. Now the question is, where did power come into play, if at all? There is nowhere in those equations that I found power - I used the motor curves to relate speed to torque, but that's it. What on earth is the power curve used for?

Thanks in advance!

[Ken Leung]

Ah, there come a point in a student's search of knownledge about speed, torque, and power of motor when he finally ask the question, "what is this power thing?"... I know this because I asked the same question last year.

As you said it, power is work over time. Its a unit of how much work can be done over certain amount of time. But Power, is also equal to force times velocity, and torque times angular velocity. Play with the equations, and you will see how those two are the same.

So, power is a measurement of how force and speed you have. Its a combination of both things. It is a measurement of how much work you are doing at each condition of speed/torque. Just look at the speed torque curve. At the end point of the curve, where the stall torque is or free speed is, you can calculate that both ends have power of zero, simply by seeing that Stall torque * zero speed and free speed * zero torque = to zero power.
In the middle is where you find maximum amount of power you can get out of a motor working in its best condition.

So what's important about power you ask? Well, with the calculation you showed, you can clearly figure out how you want to gear the motor... (you should gear it to had a load of about 1/2 stall torque for max power). But in general, when you are faced with a problem, you should figure out how much power you need to accomplish a task, and see if the motor have enough power to do it. After all, if FIRST switch to different motors, how do you know which one to use?

In your example. You know the torque you need to do the task... But at the load the motor is facing, is it moving at a speed fast enough? You have to go through the calculation and speed torque curve just to see how fast its spinning. If you do this with power, you first figure out how much torque you need to do this, and how fast you want the thing to move... Multiply those numbers, and you get the amount of power you need. Then you look up which motor have enough power for that, and you can see which motors you can and cannot use.

The important about the power curve, is that you can see where you should gear your motor at. Near the peak of the power curve is what load you want your motor feeling. The further you are away from the peak, the more power you are wasting. The wasted power usually goes into Heat and heat up your motor.


I have a lecture note from the motor workshop I give for WRRF teams in the white paper. Go through the calculation at the end, and you will see my process of figuring out the motor and gearing.

Its on the fifth page @ http://www.chiefdelphi.com/forums/pa...C&pagenumber=5

[patrickrd]

Ken hit most of the key points, but I think some simple equations would be useful.

Electrically: Power = Voltage * Current

Mechanically: Power = Torque * Rotational Velocity

Thus:

Voltage * Current = Torque * Rotational Velocity
This is only true if motors are 100% efficient at turning electrical into mechanical energy. In reality, motors are not. DC motors are extremely inefficient when they are stalled (NO mechanical energy is produced but TONS of current is being drawn), but pretty good when the load on the motor is less. That is why the motors heat up so much if the robot is in a pushing match.

Really:

Voltage * Current = Heat + Torque * Rotational Velocity

Heat = Voltage * Current - Torque * Rotational Velocity

Efficiency = (Torque * Rotational Velocity) / (Voltage * Current)

I think Ken's link is likely to provide graphs of most of these.

Now, how can we not waste this energy to heat? The answer is a transmission (continuously variable is nice, eh team 190?). If we are going to be pushing against another robot and likely to be close to stall torque, we change our gear ratio on the fly such that we provide a lot more torque and a lot less rotational velocity. This way we can push what we want to push at the expense of speed.

- Patrick

[Adam Y.]

I would like to recomend a book but one that may get me into trouble. I would probably buy Build Your Own Combat Robot by Pete Miles and Tom Carroll. It's got everything you ever wanted to know about building drivetrains, motor equations, batteries. It really does make a handy refernce book. It also explains why things act the way they do. Btw hear is a power question not related to robotics. How did watt figure out how much power is in a horse?? My physics teacher didn't tell me.

[AdamT]

Originally posted by wysiswyg
How did watt figure out how much power is in a horse?? My physics teacher didn't tell me.

I have nothing to contribute to the thread because Ken did an awesome job of summing it up, but you really are stuck on this, huh?

Here's my guess: He found an object like a stone *a stone is actually a unit of measurement* and found how many horses it took to pull x amount of stones. Now, taking that into account, you can figure out how much energy it takes, etc...

[Clark Gilbert]

The story goes that Watt was working with ponies lifting coal at a coal mine, and he wanted a way to talk about the power available from one of these animals. He found that, on average, a mine pony could do 22,000 foot-pounds of work in a minute. He then increased that number by 50 percent and pegged the measurement of horsepower at 33,000 foot-pounds of work in one minute. It is that arbitrary unit of measure that has made its way down through the centuries and now appears on your car, your lawn mower, your chain saw and even in some cases your vacuum cleaner!



What horsepower means is this: In Watt's judgement, one horse can do 33,000 foot-pounds of work every minute. So, imagine a horse raising coal out of a coal mine as shown above. A horse exerting 1 horsepower can raise 330 pounds of coal 100 feet in a minute, or 33 pounds of coal 1,000 feet in one minute, or 1,000 pounds 33 feet in one minute. You can make up whatever combination of feet and pounds you like. As long as the product is 33,000 foot-pounds in one minute, you have a horsepower.

http://www.howstuffworks.com/horsepower1.htm