JVN's Calculator (help)
 

I downloaded JVN's Calculator last night and still have not quite figured it out. Is there any way I can calculate an accurate speed with the compensation for chain and sprockets also? I've been playing around with it and haven't noticed a feature for the sort. Maybe somebody can point me in the right direction? (Even if it is someone telling me that I need to calculate that part of it myself) All help is appreciated!

Re: JVN's Calculator (help)
 

Chain/sprocket reduction have the same idealized mathematical model as gears do, so you can just fill in one of the lines under Driven/Driving Gears for the chain reduction.

Cheers,

Re: JVN's Calculator (help)
 

A 12 and 22 tooth sprocket will cause the exact same reduction as a 12 and 22 tooth gear. Plug it is as if they are gears.

Re: JVN's Calculator (help)
 

It totally depends on how precise you wan't to be, but treating a sprocket ratio as a gear ratio may be different due to gear reduces efficiency. Aluminum sprockets I believe have an efficiency of about 90 - 92 % if your using two sprockets. So if you feel like calculating things yourself :) !
__________________________________________________ ___
Gear reducer ratio = Gearbox sprocket# / Wheel hub sprocket#

Equation:

Output speed(RPM) =
Input speed(JVC outputRPM) / Gear reducer ratio * gear reduces efficiency(% ...0.92 or 0.90)

Once you have output speed(in RPM)

Calculate Circumference = Wheel diameter(in) * PI

Finally:

Speed(fps) = (Circumference * Output speed) / [60 (for seconds) * 12(get ft)]
__________________________________________________ _
I hope this isn't too confusing :D

Re: JVN's Calculator (help)
 

This is simple, but may also be simplistic. Sprockets generally reduce efficiency, but so do a host of other factors, such as motor effectiveness at different loads, air drag, rolling resistance, and more, none of which are constant. We found that our overall efficiency this year was above 90% in low gear, and less than 80% in high gear. Unfortunately, there is no substitute for testing.

Re: JVN's Calculator (help)
 

Good call.

Playing with numbers is still fun ;) especially before purchasing gearboxes.

Re: JVN's Calculator (help)
 

Could you share how you are doing this testing? What are measuring and what are you holding constant?

Re: JVN's Calculator (help)
 

We marked 20ft in 2ft intervals, then ran the robot at full throttle (from stop at the 0ft mark) in both low and high gears while capturing with a camera at 60fps. We did three trials of each gear. I then crunched the frame data and modeled some curves off of them.

Re: JVN's Calculator (help)
 

This would make for a very nice little white paper for the community showing how you adjust the model to correlate the data. Something simple and clean like a youtube video showing the acceleration and picking out the data points, and then adjusting the factors and how they move the distance vs. time curve.

Re: JVN's Calculator (help)
 

Nice. Did the wheels break traction at the starting line when you hit it with full throttle?

Could you please share a few details about the math here? How did you calculate the 80% and 90% numbers?


EDIT: just saw IKE's earlier post about posting a paper. I agree. In the meantime, perhaps you could whet our appetite with a few details as mentioned above.

Re: JVN's Calculator (help)
 

The wheels did not break traction. We're running 4 CIMs on a pretty heavy robot.

As for the efficiency numbers: The drivetrain's free speed, without any efficiency losses anywhere, is easily calculable from CIM free speed and gearbox reduction. I used the frame data to get a distance-over-time graph with 11 points of data (0ft-20ft at 2ft intervals), then ran a power regression (r^2 =~= 99.5%) to fit a curve to it. I took derivatives to estimate velocity and acceleration, but these were not too accurate because the robot hit its top speed before the end of the 20ft. How do I know that? The last 5 data points in each gear fit a line (r^2 =~= 99.9%), which I used to calculate top speed. I then compared this with the theoretical free speed of the drivetrain to find the efficiency.

After that, I talked to my physics teacher, and was able to draw all sorts of interesting conclusions about the factors that affect efficiency. I had originally hoped to come up with a differential equation that could solve for efficiency based on major factors, but after these tests, it's very clear that this equation would not only be extremely difficult to solve, but also nearly impossible to generate in the first place. I might expand on these points in a future white paper, but I have a lot on my plate at the moment. Hope this helped.

Re: JVN's Calculator (help)
 

@T^2:

So bottom line, if I read you correctly, to get the efficiency numbers you measured the vehicle top speed in each gear, and divided that by the calculated vehicle speed at CIM-free-speed.

That's an interesting method. It also helps explain why you got a higher efficiency with more gears.

@all:

What "efficiency" metrics and test methods do other teams use?

Re: JVN's Calculator (help)
 

Could you explain this statement?

Re: JVN's Calculator (help)
 

Sure. By "more gears" I meant more gear reduction, i.e. more speed reduction.

In an earlier post you said:
In low gear your top speed is slower, so the forces and torques at steady-state at full throttle are lower compared to high gear at steady-state at full throttle.

Re: JVN's Calculator (help)
 

I agree with this statement. However, lower torque is not the only factor contributing to loss of efficiency at higher speeds. We found that our effective gearbox spread was lower than 2, while the theoretical spread was 2.27. In my opinion, additional loss of speed should be taken into serious account when designing multi-speed drivetrains; this applies to JVN's calculator in particular, since it is so widely used. It allows for a "gearbox efficiency" number on top of a "speed loss constant" -- but neither of these numbers are anywhere close to being actual constants.

Re: JVN's Calculator (help)
 

For the record, I said forces and torques.

The additional reduction in your observed top speed is caused by these higher forces and torques: the higher force required to sustain the higher vehicle speed ultimately manifests as higher torque load on the motor which in turn means the motor spins more slowly... and thus the steady-state vehicle speed is reduced. Since you are calculating efficiency by dividing measured steady-state vehicle speed at full throttle by theoretical speed based on CIM free speed, that's why you get a lower efficiency number for high gear.

Re: JVN's Calculator (help)
 

Ether - are you suggesting that there is a more meaningful or relevant measurement?

Reading this thread has made me think - what are we trying to calculate and what do we care about? It seems that actual top speed is a very relevant piece of information. There are certainly limitations to oversimplifying drivetrain design to a single spreadsheet with several assumptions that try to bridge the gap from theoretical to actual.

Re: JVN's Calculator (help)
 

No. It's undoubtedly an excellent metric at top speed.

How would it be used, and how accurate do you suppose it would be, to predict behavior at low-speed high-torque operating conditions?

And, since the title of this thread is "JVN's Calculator (help)", how would one go about using that single metric to derive the 2 free parameters "Speed Loss Constant" and "Drivetrain Efficiency" in JVN's model, so that the model could be used to analyze other operating scenarios?

@T^2: Just wondering: did you try playing around with the 2 free parameters in JVN's model to see how well you could get it to match your measured position-vs-time data from the video?

Re: JVN's Calculator (help)
 

I dug up the actual numbers. We had an overall 72% efficiency (using motor free speed metric) in high gear and overall 92% efficiency in low gear. I then pulled some assumptions out of where the sun doesn't shine: 98% efficiency in each stage of the gearbox, with three stages total, gives about 94% gearbox efficiency overall. (Obviously, that number is not a true constant, but I assumed it was pretty close.) This leaves the speed loss "constant" as 76% in high gear and 97% in low.

For those of you in the peanut gallery, this leaves a very important conclusion: It is almost impossible to calculate the true top speed of your robot from theoretical numbers, given the sheer quantity of resistive forces involved.

Hopefully this deters teams from posting their robot's top speed without actually testing it.

Because you should. Test it.

Re: JVN's Calculator (help)
 

Would you be willing to post your actual test data? I'd like to play around with JVN's model and see how well it correlates with your test data using the above model parameter values.

Re: JVN's Calculator (help)
 

Column 1 is high gear time, in seconds; column 2 is low gear time, in seconds; column 3 is distance, in feet.

Re: JVN's Calculator (help)
 

Voltage drops are another thing to consider, and there's more...

The "speed of light" value for a drivetrain is given by the kinetic energy at a given speed -- you can't possibly get to speed any faster than given by E = 1/2mv^2; time here refers to how quickly a given amount of energy can be added to the system. This suggests that measuring time to velocity could yield a meaningful measure of overall efficiency. You can figure the maximum mechanical energy you can put into the system as follows (taken from small portion of a paper I'd like to post at some point, but it needs work):

A CIM at max. power consumes 12V * 67.9A or 814.8W. Mechanically, it puts out 337W, so it is only 41% efficient at this operating point. This can be derived by converting 171.7 oz.-in. / [16 oz./lb.] / [12 in./ft.] * 2655 RPM * [2π rad./rev.] / [60 sec./min.] / [1.356 (ft.-lb./sec)/W] = 337W (it is important to watch the significant figures, but being a bit sloppy here). This is a good occasion to point out that lb. is both a unit of mass and also of force. This is unfortunate and can be confusing. Paying attention to units is a good cross-check and SI units avoid this problem. Notice the assumption that we can get a steady 12V. This also ignores things like a CIM possibly being less efficient if it becomes hot. So the energy (in Joules) of an ideal CIM running full out (this only happens at one point on the motor curve) is 337W * t (in seconds). The raw numbers here are all either conversion factors, or taken from the CIM datasheet at 12V, running at the maximum power point.

If you know the mass of the robot and the velocity, you can find the kinetic energy. Knowing the number of motors and the time, you can determine how much energy could possibly have been added, under ideal conditions. The overall efficiency is given by the ratio between the two numbers, but this is going to be a harsh metric. It does point out some of the places efficiency is lost however. For example, keeping the motor near the ideal operating point would require a continuously-variable transmission; for a two-speed transmission, you could not only measure the effect of shifting while accelerating but also try to figure out when to do this. One take-away is that the gear ratio can impact efficiency in a major way, so the total picture is more than just the fraction of the mechanical power that makes it through a gear/chain train.

One of the main points of the Calculator is to show that a drivetrain is more than just a speed calculated when the CIM is running at a certain point -- a drivetrain has to get you to this speed in the available time and distance.

It would be good if there were some recognized way to measure efficiency of a drivetrain, so drivetrains could be compared in this way. But this does begin to illustrate how the electrical system plays a role, and not just the design but also how well adjusted and maintained all of the mechanical elements actually are will affect losses. In the end, a simple parameter in the model that can be adjusted to match observation is very helpful, along with understanding where all of the losses happen and how to minimize them...

I hope this is helpful -- if I ever get the full write-up to a good point, I'll post it, trying to incorporate feedback.

Re: JVN's Calculator (help)
 

Another factor worth noting is that the JVN spreadsheet ignores motor acceleration and instead focuses on steady state top speed. How much time and distance it takes to get there are very important, especially in years when the competition floor is divided into different zones.

A spreadsheet is a great tool for certain things but also has it's limitations. Has anyone ever endeavored to make a more advanced tool that factors in more of the dynamic variables such as motor efficiency?

Re: JVN's Calculator (help)
 

1. I feel like the list of significant variables would quickly become overwhelming.
2. The differential equation this would create would be nearly impossible to solve, especially if you want acceleration.
3. Those variables don't usually follow well-known equations anyways.

Re: JVN's Calculator (help)
 

Don't despair. A Scilab model like this can solve your problems. Just break the problem down into it's parts.

Here:
-There is only one first order differential equation of consequence.

-The inputs you need are actually fairly well known. Real CIM motor torque curves are already out there... The individual gearbox properties are basically two numbers and you can get these from component testing which is not more complicated than what you are already doing with the robot. And if you're using the same/similar final drive as a previous year, you should know plenty about the performance before you build it. The ability to predict the final top speed and acceleration profile of a new robot will be as accurate as your production process is repeatable.

This simple Scilab model can be extended to include differentials, planetary gear boxes, shifting transmissions, improved motor models, electrical dynamics, traction stick-slip, and/or coupled to a 6DoF robot chassis model...

The key limitation is that this approach applies a lumped inertia model (motor and transmission lumped to the wheels) so the torques at the individual meshes are smaller than they should be (and therefor the losses are smaller) when the system is back-driven. But it is still a very good modeling approach.

EDIT: Updated the linked file. Bug fix in the gear box. My apologies to those who have already downloaded. Since the speed and torque are solved in opposite directions within the gear box, the torque should not have used 1/gear_ratio.

Re: JVN's Calculator (help)
 

Note that if you have something like an encoder that can measure position and velocity, an interesting thing to do is to collect data from a dead stop to maximum velocity. At maximum velocity, all the energy being put into the system is being used to offset various losses, so you are 0% efficient. The maximum velocity, time to maximum velocity, and distance to maximum velocity numbers reveal something about the performance of the overall drivetrain. If you know the mass of the robot, the velocity data also yields the kinetic energy at each data point that is sampled (1/2mv^2).

With the new power distribution board, it should be easy to also sample the voltage and current for each motor in the drivetrain. The product of these two is the electrical power being used by each motor. Integrating this over time gives you the total electrical energy that has been put into the system, so you can come up with an efficiency (kinetic energy/total energy input). In practice, the power at each sample would be multiplied by the reciprocal rate (if there are 10 samples per second, this is 0.1 second) and these products summed across samples. This gives you efficiency to maximum velocity, a fourth number that is potentially interesting to compare. A really good drivetrain might get into double digits here...

You could also use the velocity of each motor and the voltage and current at each motor to derive the torque at each motor, so you could look at the mechanical energy being put into the system and compare this with the kinetic energy and the electrical energy. This should allow you to see the mechanical efficiency. Monitoring all of this could let you know when something is not right in a drivetrain (electrical or mechanical), and also help to iteratively optimize the design of a drivetrain, derive parameters to use in the drivetrain model, etc.

If anyone has or can easily get this sort of data, it would make a neat paper, with graphs of this data from stop to speed.