28Jan2015: Lots of the material below is relevant for 2015. However we probably won't be using force sensing resistors (FSR) to measure contact forces
On this page... (hide)
- 1. Testing Fine Points
- 2. Analysis Fine Points
Note: If you want a pretty good estimate of the motor+gearbox performance under "realistic working conditions" you can stick a pulley on the motor shaft and lift a weight using a string. The output power is mg*v_y where v_y is the upward velocity of the weight. The input power is V*i. So you know enough to compute efficiency of the motor and its little internal gearbox immediately.
Since stall currents, no load currents, R and K were given to us in the Lego Motor Characterization Sheet, are we allowed to use that information instead? or were we supposed to collect data for all of that on our own?
Yes you can use them to get R and K, and... You will still want to do a 6 volt no-load and perhaps a pulley test of your motor anyway because otherwise you will have no idea how much power is lost in the little 24:1 internal gearbox in the motor. (Marcus' measurements are only for the base motor, removed from its gearbox).
For this resistance, is it better to test each wheel individually?
No, you can get an aggregate rolling resistance. (What would need to be tested individually is if you are rolling wheels over the pressure sensor to get an idea of the normal reaction force.) For rolling, try to test with crawler loaded as it would be loaded when driving. So if it uses rubber bands for clamping, leave them on, etc.
Try rolling with final gear stage disconnected, so you aren't back-driving the transmission, and find how much force is needed to pull it along the track. This will be rolling resistance plus any sliding of guides +brushes along the track. Refer to the Crawler notes from Jan 29 for equations about this. The rolling resistance is slightly different (see "Power Loss Assessment" section) when pulling than when driving.
You can also repeat the test with the final gear stage connected to see how much extra power that requires.
Recall that "rolling resistance" is not the same as the coefficient of friction between the tire and the track. The rolling resistance is due to hysteretic losses in the tire; friction is what governs how much tangential traction force you can get for a given normal force (see FBD section below).
There is now a Wikipedia entry on rolling resistance: http://en.wikipedia.org/wiki/Rolling_resistance
The FSR data isn't terribly accurate for our purposes, but it is the only way for you to get a rough handle on the normal forces in your system if your system is not statically determinate (i.e., if you can't immediately estimate the normal forces from knowing mg). See the FSR calibration data on CrawlerNotes and Coursework. Best to run over it several times if using it.
You might like to reduce friction in your mechanism. The most likely source of it will be where the little black Lego spine shafts are spinning in holes. The first, best thing is to reduce any misalignment so they spin loosely. Beyond that, you can apply a little bit of Vaseline or chapstick (which is very similar). A little graphite (like used on sticky key locks) is another possibility. In any case, all these measures are probably less effective than having a solid, well-braced and properly aligned structure in which the axles are not heavily loaded.
Avoid spraying anything -- it gets all over where you don't want it (Tires!!) as well as where you do. WD-40 is a penetrating solvent, good for helping free rusted bolts. So it penetrates into all your Lego bricks and helps them to unsnap. It also evaporates quickly so you keep having to spray more and getting it where you don't want. It's also possible that WD-40 and other solvent-containing lubricants could attack the Lego ABS plastic. Note also that almost all oil-based lubricants will attack rubber bands.
We will take 3 sets of measurements:
- P1 = typical power (Volts x amps) while climbing, sans bobsled
- T1 = time to go a certain distance while climbing, sans bobsled
- We will probably measure for a distance somewhat less than the actual total distance of this part, and then adjust the time correspondingly.
- P2 = typical power while climbing, with bobsled
- T2 = time to go a certain distance, with bobsled
- P3 = typical power while descending, with bobsled
- T3 = time to descend a certain distance
Energy = Sum(P_i * T_i)
It could be possible... Even if your transmission is not "back-drivable" it might be close enough to back drivable that the motor is getting some help in spinning. Hence it doesn't have to fight its total friction (motor + little internal gearbox). In any case, if you measure 6 volts and a current on descent that is actually lower than the corresponding no-load current for the motor, that's what we have to conclude.
Caveat: We're talking here about the no-load current of the motor including it's little internal gearbox, right? See notes about "This Year's Motors" for details on Coursework and attached here for convenience.
When the crawler is descending with bobsled the measured current is low enough that it doesn't appear on our plot of Power and Efficiency (motor rpm's are too high). It seems this indicates our motor is resisting the crawler's movement down the track, keeping it from accelerating due to gravity. How can I account for this in the report on our power and efficiency plots–should we mark the efficiency and output power of the motor as negative?
Yes, if we understand your email, you are not the only team with this problem. It is entirely possible that the motor speed is higher than the corresponding "no load" speed at 6 volts and the current is lower than the "no load" current at 6 volts. Is that what you are saying? If so, it means you are almost back-drivable or perhaps marginally back-drivable. Enjoy!
We are not really looking much for analysis of the downhill part of the event because (as we showed in class today) it has little effect on the total energy consumption. You can explain what is going on and leave it at that.
Is transmission efficiency a scalar or a constant power loss?
Transmission efficiency (to be specific Pout/Pin for a geared transmission) can be reasonably well modeled to be a constant percentage (that is, if you have a transmission which is xx% efficient, you can expect for any power you put in, Pin, you will get out Pout = Pin*xx%).
You could test this by measuring your transmission efficiency at several different input powers with something like a winch test. Wrap some string around a drive wheel or pulley on the output axle of your transmission. Lift a weight (mg). Measure the vertical speed v_y. This is the output power, with no rolling resistance or slippage.
For the redesign section, we are mainly looking for an intelligent explanation why a lower or higher gear ratio might make your design work better while climbing. We don't really care about the descending part. See section below of Power versus Energy. Now, if you want to be more systematic about the analysis, you can do this:
1. We know that, roughly speaking, the force required to propel the vehicle up the track does not vary much as a function of speed. Why? Because gravity is constant and rolling resistance is (supposed to be) independent of speed. And slippage also perhaps does not vary with speed (or at least not a great deal for the range of speeds that we can reasonably go).
2. Given (1.) above, this means that the torque required at the drive wheel also should not vary much as a function of speed.
3. So then, the torque required from the motor is just a function of your transmission ratio. The higher the gear ratio, the lower the required motor torque. The lower the gear ratio, the higher the required motor torque.
4. For a given torque required out of the motor, this means that the current in the motor is immediately known, because k*i is what produces torque (minus Tlf, which is constant).
5. For a given current, and while running at a particular speed, the efficiency and power consumption of the motor is known.
6. This means that for various transmission gear ratios, you can compute the corresponding motor current (and speed) that will produce the necessary motor torque. And knowing these, you can easily compute input power * time. So, you could do this for a range of transmission ratios from a reasonable lower bound of about 2.5:1 to an upper bound of perhaps 20:1.
7. Note that the lower bound on gear ratio is absolutely limited by the the motor stall torque. You can't get any more torque from the motor than that! And the upper bound would be limited by the motor no-load speed, but at that point you are going so slowly that you take forever to get up the track.
Although the motor notes (and most motor literature) focus on efficiency, what is going on with this project is a bit more complicated. We are trying to reduce the total energy consumption to travel a given distance, where:
Energy = Power*time = Power*(distance/speed)
Some elements, like the motor, have an efficiency that varies strongly as a function of speed. And the motor is pretty inefficient (like 50% at best), so it's a big factor. Other elements like the transmission and rolling resistance have efficiencies that are (theoretically) independent of speed. And then there is slippage: v_slip = (r_w*omega_w - v_x). It's not clear how this varies with speed. Maybe to a first approximation it's constant? This is probably the most reasonable assumption over a limited range of reasonable crawling speeds.
So you could use Matlab or Python to compute an estimated total power loss (motor+transmission+wheels+slip) as a function of speed and then see how this varies as a function of changing the total gear ratio, N. Then look at total energy consumption to climb a certain distance.
What are the limiting factors?
- obviously, omega cannot be higher than omega no-load at 6 volts, and the input current cannot be lower than i_nl
- obviously the available motor torque cannot be higher than (K*i_stall - Tlf), and even this is only if the velocity goes to zero.
3. Differences between theoretical and actual wheel speed are only due to slippage at the wheel. Remember that gears in mesh must obey the relation omega2=omega1/N, where N is the gear ratio. The losses that you may be thinking of are only realized in torque output, such that t2= t1*N*η, giving the expected overall power relation of P_out = P_in*η=omega1*t1*η. Again, since speeds at places other than where the wheels touch the shaft are strictly governed by the gearing ratio, all of these other inefficiencies are simple torque losses, not speed losses.
Note that it's up to you where to put the rescuer weight and where to attach the arm or string for the bobsled. It's a design decision.
The FBD helps you to see if the normal forces are actually greatest under your drive wheel (which is what you want). And when you catch the bobsled, does your drive wheel have a greater normal force (good)? Or less (bad)?
We ask for both a Side view and a Top view because the bobsled is off to the side of the crawler track and a side view doesn't catch this.