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 :) !
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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)]
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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.