Gearing and all that....

[bsodmike]

Hi all,

This topic has been discussed ad nauseam but do bear with me as I'm interested in both the theoretical and practical aspects.

There are many guides that talk about gearing, wheel circumference, and a calculated top-speed.

To start off, I'm going to take my Kyosho as a base reference running Bad Lands, with an OD of 117 mm. I'll be using the x10^(-3) notation to refer to 'mm', so 117x10^(-3) m.

Circumference is calculated as 2πr (r=wheel radius) or πd (d=diameter). So our circumference is π117x10^(-3) m. It's a direct pinion/centre diff (spur) setup, so the FDR is simply 12T pinion:46T spur which works out as 46/12 = 3.83 rounded to 2 d.p. This means every 3.83 revolutions of the pinion, the Spur makes a single revolution. The link I posted at the beginning has got this fact wrong in their article; the pinion is smaller, it has to turns many more times to get the spur to complete one rev. So 1 motor rev = 1/3.83 spur revolutions.

Q1. Does one complete revolution of the center CVD-axels translate to a full-revolution at the wheel knuckles? I'll check into this tomorrow.

Roll out is defined as wheel circumference/gear ratio. Therefore this can be calculated one of two ways:

1. π117x10^(-3) m/3.83 = 95.97 mm/motor rev roll out

2. π117x10^(-3) m*(12/46) for the same result. This is just simple algebra, i.e. x/(1/2) = 2x

I also thought of the 'ideal' case without any gearing at all, i.e. the pinion is the same size as the spur, a 1:1 gearing. This works out to 367.57mm/motor rev roll out. 367.57/3.83 = the result we got previously, so that's a decent check.

I won't get into the maths on the theoretical top-speed calculation but it works out 132.23 mph running 2,200 kV * 16.8V(4S on full-charge) = 36,960 motor RPM. However, I will note that it means the spur gear/centre axels will rotate at 36,960/3.83 = 9,650 RPM.

From the various articles I've searched to forum posts I've seen, there has been no reference to wheel mass, inertia, and the energy required (torque) to rotate the wheels from rest. The RC mass would also play into such considerations.

I've seen comments for increasing the tooth-count on the pinion gear have people say 'you're trying to run it at too high an RPM, hence it's getting hot'. Say going from 12T to 19T pinion - less torque, more-top speed.

Q2. Why does gearing the pinion lower cause the motor to get hotter, doesn't the RPMs we demand via the throttle determine the motor RPM? That said, one way to look at this is in terms of work-done and roll-out. A longer roll-out (say we increase the size of our tire's OD) means the RC will travel a longer distance per motor rev. Work = Force*distance, therefore the motor has to do more 'work' per rev. Thoughts?

It also makes me thinking about motor physics; starting a motor on a high-load needs a high in-rush current. Once a BL motor reaches continuous velocity (say you're cruising at constant speed) then the current-draw is minimal; these surge current spikes will happen when we blip the throttle to max! The ESC is a limiting factor in terms of max current available to the motor and this would be the limiting point as to the max weight of the buggy/wheels a BL motor could power.

I guess I'm interested in more (theoretical) details on the 'limits' and factors resulting in hotter motors. Practical details from our veteran RC'ers is also much valued.

Thanks again for your time.

Cheers M.

 

[Non Crimen]

Whoa. Haha. I never go that in deep in things. I don't know what to say....


Sent from my Pipboy-3000 in the Capital Wasteland.

 

[2revo1maxx]

Hi all,
Q1. Does one complete revolution of the center CVD-axels translate to a full-revolution at the wheel knuckles? I'll check into this tomorrow.
Cheers M.

No. There is a pinion gear turning a ring gear in the differentials. I don't know any specific tooth counts, but on most rigs that accounts for roughly half of all the gear reduction between engine and wheel.

Excuse me if I'm wrong, but isn't tire circumference calculated by multiplying the diameter times pi (3.1415926535)? Most rc tires have the diameter stamped on them already.

I think you should simplify your explanations and theories a little so some of us regular people can understand.

 

[bsodmike]

*duplicate* pls remove.

 

[bsodmike]

There is a pinion gear turning a ring gear in the differentials

Ok so you're on about the pinion and spur gears - I've detailed those above as being 12T pinion and 46T spur.

Right, so what made me even *think* it's possible that a single turn of the center shafts results in a full-rev at the front/rear axels? Well, it's the definition of calculating roll out:

"Roll out is defined as wheel circumference/gear ratio." or taking it's alternative form, roll out = (pinion/spur) * wheel circumference. The pinion/spur fraction is the number of turns the centre shaft makes in relation to one full-revolution by the motor, i.e. 1 pinion turn = 12/46 = 0.26 turns of the spur gear. Therefore, it's implied we travel almost 1/4th the wheel circumference.

Excuse me if I'm wrong, but isn't tire circumference calculated by multiplying the diameter times pi (3.1415926535)?

See above where I've done:

"Circumference is calculated as 2πr (r=wheel radius) or πd (d=diameter). So our circumference is π117x10^(-3) m."

You are correct - you'll notice the symbol for pi is in front of the diameter (now in meters due to being in scientific notation). This way, we can perform the final computation of pi much later on.

Mmm, OK I'll certainly try. I tried keep my theoretical part as brief as possible, although it seems on my quest for brevity I've introduced complexity.

I'll break this down in a bit.

 

[2revo1maxx]

Ok so you're on about the pinion and spur gears - I've detailed those above as being 12T pinion and 46T spur.

Right, so what made me even *think* it's possible that a single turn of the center shafts results in a full-rev at the front/rear axels? Well, it's the definition of calculating roll out:

"Roll out is defined as wheel circumference/gear ratio." or taking it's alternative form, roll out = (pinion/spur) * wheel circumference. The pinion/spur fraction is the number of turns the centre shaft makes in relation to one full-revolution by the motor, i.e. 1 pinion turn = 12/46 = 0.26 turns of the spur gear. Therefore, it's implied we travel almost 1/4th the wheel circumference.

 

[bsodmike]

I just realised the 'missing' piece of what's been puzzling me - it's how incomplete lot of these 'gearing/rpm' guides are in technical terms. In practical terms, it makes sense to talk about gearing in terms of smaller pinion/larger spur = more torque, but the point is this is 'perceived torque'!

@2revo1maxx Prime is right, thinking about roll out was the key. Running an RC with larger wheels, increases the roll out; in terms of the motor it means that for each motor revolution, the RC travels a further distance. Going back to the concept of power, Power (in Watts) = Force * distance travelled, shows that we'd need more power since we are still working in reference to a single motor turn! And that's why the motor heats up, more power output means more current is drawn. This answers Q2.

Also going back to torque, I remembered there was a relationship with armature current; generally it's safe to say that torque is proportional to the current supply, although in reality there is a torque ripple. Rather than going into specifics, more current drawn yields much higher torque.

The misnomer is that in the RC world we're taught to relate torque with gearing - hence my calling it 'perceived torque' as this is not related to torque at the motor shaft, but rather torque felt at the wheels. This is perceived torque is in terms of FDR, it's a fair way to make it simple enough for all to understand, i.e. it's far more intuitive.

What about the mass of the wheels and RC, say you? Well, think of the effort the motor must put into turning the Spur gear. The Spur gear is initially at rest and turning it requires a certain amount of torque... aha! So heavier an RC and/or heavy wheels will certainly make it harder for the motor to turn the spur gear from rest. Bigger the 'load' more armature current is needed to over come it. Say we make it such that the motor shaft cannot be turned by the motor - NEVER DO THIS!! - this has the motor act as a short-circuit, essentially drawing infinite current.

I found a rather nice writeup at Castle Creations that gets slightly technical and much easier to understand than much of my rambling
http://www.castlecreations.com/support/max_tuning_guide.html

It's good to note that higher quality batteries will yield a far better 'torque' at the motor-shaft, also lower voltage sag under load say with Turnigy nano-tech's (or so I hear).

For anyone here interested in the study of DC motors (falls under electronic and electrical engineering domain), this is a decent write up:
http://control.disp.uniroma2.it/zack/LabRob/DCmotors.pdf