Best Pulley Gearing Ratio Eboards?

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Best Pulley Gearing Ratio Eboards?

Postby torqueboards » Thu Aug 22, 2013 1:20 pm

What's the best gearing ratio for small motor pulley to drive hub pulley? How does it work? What would be the best gearing for medium speed? I'd like to learn more about gearing ratio as I am working on creating a motor mount and would like to understand the process more thoroughly.

If anyone can help would be great. I'm sure it would help others when starting their build as well.

What's your ideal gearing ratio setup for small motor pulley wheel & drive hub wheel? How many teeth? What would be your ideal setup for top speed? What would be your ideal setup for high torque low top speed? Is it worth it to use 15mm belt width versus 9mm belt width? Is distance from motor pulley to drive wheel better closer or further?
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Re: Best Pulley Gearing Ratio Eboards?

Postby Nikimce » Thu Aug 22, 2013 2:01 pm

Yes it would be excellent if someone could shed some light on this topic. I would like to know exactly the same things.
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Re: Best Pulley Gearing Ratio Eboards?

Postby PracticalProjects » Thu Aug 22, 2013 4:07 pm

Yeah well it depends on your use, If you are in an area with lots of hills you obviously will need more torque so a higher ratio will be needed, it doesnt really matter how many teeth if you keep it in the same ratio, for example for a very high torque setup of 1:5 you could use 10T to 50T or 6T to 30T etc, however with this your top speed will be pretty low. With my setup I went for a higher power lower kv motor which will naturally have more torque in itself. So i used 8s lpoly at 29.6V, with this and the kv of the motor you can calculate the boards theoretical top speed. My motor at 213 kv means that the motor will turn at 213rpm per volt. Theoretically my motor should turn at 6,304.8 Rpm at this voltage. So at a 1:3 ratio the rpm at the wheel of 70mm will be approximately 2101.6rpm. Theoretically the board would travel at 27.73 Km/h but this is not allowing for factors such as my weight, terrain and various other opposing factors like friction for example. The gear ratio may be slightly different to this but this is an approximate calculation. You can use this calculator to help you http://www.onlineconversion.com/wheel_surface_speed.htm I'd like to thank 'Things' for their help on this.

Hope that helped a bit, I think thats right
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Re: Best Pulley Gearing Ratio Eboards?

Postby torqueboards » Thu Aug 22, 2013 4:42 pm

Awesome. Does it matter how many teeth are attached by the belt?

What kind of top speed would a 1:5 gearing ratio get you? What is the formula for top speed?

What would be better 10T/50T or 6T/30T?

What type of gearing ratio would you use for higher top end speed?

How does the wheel size play in on the formula and is there a formula for calculating the Top Speed?
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Re: Best Pulley Gearing Ratio Eboards?

Postby Murfix » Fri Aug 23, 2013 1:07 am

Hey guys,

- The ratio is usually defined by choosing a top speed after choosing a motor and battery. Keep in mind that the higher the top speed, the lower the torque will be.
- The number of teeth will be restricted by the diameter of the gear (can't be too large). Apart from that, the more teeth on the gear, the less strain on the belt (since it's pulling on more teeth at the same time, dividing the strain), but you shouldn't worry about that, just pick a good diameter.
- You can calculate the torque you will have using the formula T = Ki * I where T is torque, I is current (max current will result in max torque) and Ki = 1/kv (that's the well known kv-rating of the motor). I didn't do this, since the top speed is more important to know in advance and the torque doesn't say that much since it's hard to estimate how much torque you will need (you have to estimate road friction, air drag, ...).

So
torqueboards wrote:... What would be the best gearing for medium speed?
When you have the motor and battery and you define for yourself what 'medium speed' is, you can go to the calculations.
torqueboards wrote:What would be better 10T/50T or 6T/30T?
For the belt, 10/50 would be better, but you should go for 6/30 since it's lighter and smaller. The belt can handle it :) Actually they're both bad choices though! You want the 'smallest common multiple" of the teeth to be AS LARGE AS POSSIBLE (http://www.mathsisfun.com/least-common- ... -tool.html). I can explain this in detail, but summarized it means that the wear will be equal on all parts of the belt and gears. This means 9/50 is better and 11/50 is even better!

Quoting myself from another topic, here's how to calculate the ratio:
"Usually you chose the gearing ratio last, as there aren't many restrictions. When you have the battery (V) and the motor (kv) chosen, you know the max RPM you will be able to get out of it (voltage [V] * kv [V/RPM] = speed [RPM]). The next step is to calculate the circumference of your wheel (let's say C = Pi * diameter). If you put your wheel directly on your motor it'll spin at for example 4000 RPM. With a C of let's say 0,5m you will travel 0,5m per round of the wheel, thus 2000 m/min or about 33,3m/s, or about 120 km/h --> WOW! Now you chose the max top speed you'll want (let's say 40km/h) and you just pick 120/40 = 3. Of course there are losses to be considered and the actual top speed will be lower so you pick a slightly lower ratio, or you agree on a lower top speed (perhaps 35km/h). Also, keep in mind that top speed = 1/torque meaning that if you want twice the top speed, you'll have half the torque!"
Last edited by Murfix on Fri Aug 23, 2013 1:10 am, edited 1 time in total. View post history.
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Re: Best Pulley Gearing Ratio Eboards?

Postby torqueboards » Fri Aug 23, 2013 1:54 am

Trying to work your formula.

30km or 18.6 miles - I'm happy with about 18 miles per hour.

BATTERY
2x 8000mah 3S 30C - http://hobbyking.com/hobbyking/store/__ ... P_30C.html

MOTOR
2x NTM Prop Drive 50-60 270KV / 2400W - http://hobbyking.com/hobbyking/store/__ ... 2400W.html

Calculating Torque - T = Ki * I. This would mean Max Current (90A) x (KV Rating) 270KV = 24300?

MAX RPM = Voltage * KV = Speed RPM
22.2V * 270 = 5994 Speed RPM

80mm Wheel
C = 3.14 (Pi) * 80 (mm wheel) = 251.20

Ahh I'm confused :)
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Re: Best Pulley Gearing Ratio Eboards?

Postby Murfix » Fri Aug 23, 2013 7:44 am

You're on your way :-)

First of all: Ki = 1/kv ! It's the inverse, not the same. You can google more info on it if you like.

If your C is 251.20mm, that means that you will travel 0.2512 meters forward if your wheel spins 1 round, right?
The motor will spin at 5994 RPM so if your wheel would be attached to your motor, it would also spin this fast! 5994 spins/minute and 1 spin = 0.2512 meter, so that would be 1505.70 meters/minute --> 90.342 km/h (sorry, I'm using the metric system). Wow, that's way too fast! That's why we use gears, in this case, to slow down. You want 18 mph, that's about 29 km/h. So 90.342 / 29 = 3.11 --> that's your gear ratio! If you pick 12:37 teeth, you'll get 3.08 and a very nice 'least common multiple'. Please note that this is the theoretical top speed, I'm using a total system efficiency of about 70% (all losses included). So if I were you, I'd start from a top speed of 29/0.70 = 41.43 km/h to compensate these losses and actually ride 29 km/h. This means 90.342 / 41.43 = 2.2, perhaps 23:10 teeth. This sounds lower than other people on the forum, maybe they didn't discount the losses, maybe I'm estimating in a pessimistic way, I don't know =)

Good luck!
Memo to myself: Screw it, just do it!
1 Apr 2013 - Start pre-engineering my first EV build!
6 Aug 2013 - Ordered all parts for my Emtb 8s 2x2kW 270kv Alien ESC setup.
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Re: Best Pulley Gearing Ratio Eboards?

Postby torqueboards » Fri Aug 23, 2013 8:11 am

Awesome. That clears it all up. :) Thanks again Murfix! The descriptions helped.

Maybe, you can help with this one too. How do I calculate my average distance on my battery?
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Re: Best Pulley Gearing Ratio Eboards?

Postby Murfix » Fri Aug 23, 2013 8:37 am

torqueboards wrote:Awesome. That clears it all up. :) Thanks again Murfix! The descriptions helped.

Maybe, you can help with this one too. How do I calculate my average distance on my battery?

Hmm that's a bit more tough..

Volts [V] x capacity [Ah] = Energy [Wh]
6s = 22.2V
2 x 8000 mAh = 16Ah (doesn't matter if it's in series or in parallel for total capacity)
--> 22.2 * 16 = 355.2 Wh is the total energy in your battery, meaning you can continuously pull 355.2 Watts for an hour straight from a full battery to discharged state.
Then, you should have the average 'amp consumption' by the motor. Suppose you're running a 1 motor setup which needs a continuous 40 amps (just making up a number here, maybe someone can do a better estimation), at 22.2V this means you'll be needing 22.2 x 40 = 888 Watts continuously. If you divide 888/355.2 = 2.5, you'll find that you can ride for 24 minutes at this rate (= 60 min./2.5). Then you would have to know how fast your average speed is at 40 amps, I'd try to get this value experimentally, or from a similar build's data. If you're riding 30 km/h for 24 minutes, you'll have a distance of 12 km on 1 battery charge.

EDIT: sorry to have made you read all this, but I think this is not entirely correct. Calculating how much Watt you'll continuously need, I assumed that there would always be 22.2 V on the motor, which is not the case... Does anyone have a better way to calculate this???

To compare, for E-bikes you can find that riding really hard with the motor will result in a consumption of 15-20 Wh per km, so with 355.2 Wh, that would mean 17.8 up to 23.7 km.
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Re: Best Pulley Gearing Ratio Eboards?

Postby PracticalProjects » Fri Aug 23, 2013 2:03 pm

great response murfix! That definitely should have answered your question :) some people like to have the most teeth that will fit on there wheel because they believe that it is better and stronger this way as there is more belt in contact with the cog. I'm not exactly sure if this helps much but it is certainly a logical view.
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Re: Best Pulley Gearing Ratio Eboards?

Postby torqueboards » Fri Aug 23, 2013 2:53 pm

Thanks Murfix. Your a wealth of knowledge.
@PracticalProjects - Yeah, I'd prefer more teeth.
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Re: Best Pulley Gearing Ratio Eboards?

Postby sn0wchyld » Sat Aug 24, 2013 9:08 pm

PracticalProjects wrote:great response murfix! That definitely should have answered your question :) some people like to have the most teeth that will fit on there wheel because they believe that it is better and stronger this way as there is more belt in contact with the cog. I'm not exactly sure if this helps much but it is certainly a logical view.


The only reason for most teeth on the wheel is to get the most teeth on the drive shaft of the motor... The more teeth there, the more efficient, quiet and long lasting the chain is. 12 is usually considered a good minimum, though thats only a guide.

Murphix, thats a pretty good way to estimate range. Theres too many variables to get more accurate than that.
For those looking for a rough idea on range... I get about 45m to an hour from my mountainboard with mixed riding. 5s 20ah lipo... About 350wh useable power. Twin motors. They draw about 6-8 amps each at cruising speed, flat hard ground/ashphelt. About 80 peak when flooring it from low speeds
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Re: Best Pulley Gearing Ratio Eboards?

Postby PracticalProjects » Sun Aug 25, 2013 3:24 am

ahh right,thanks
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Re: Best Pulley Gearing Ratio Eboards?

Postby Murfix » Mon Aug 26, 2013 2:36 am

Thx for the positive feedback and confirmation! ^^
Memo to myself: Screw it, just do it!
1 Apr 2013 - Start pre-engineering my first EV build!
6 Aug 2013 - Ordered all parts for my Emtb 8s 2x2kW 270kv Alien ESC setup.
3 Sept 2013 - All parts have arrived: on to the build!
23 Sept 2013 - First test ride: AWESOME!
7 Feb 2014 - Upgrade finished: 3kW motors, 12S Alien ESC, entire new drivetrain and LED's!
Build topic: viewtopic.php?f=35&t=52390
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Re: Best Pulley Gearing Ratio Eboards?

Postby torqueboards » Sun Dec 01, 2013 11:07 am

Hate to bring this from the grave. Murfix, How does having two motors change the top speed? I was able to figure out all the details you listed with 1 motor. When adding a 2nd motor does it increase speed?

Example.

Here are my stats with a 6374 SK3 Motor on 12S.

133.26 km/h / 80.4672 km/h = 1.65 --> That's your gearing ratio for 50mph.
133.26 km/h / 75.4205 km/h = 1.76 --> That's your gearing ratio for 45mph.
133.26 km/h / 96.5606 km/h = 1.38 --> That's your gearing ratio for 60mph.
133.26 km/h / 66 km/h = 2.01 --> That's your gearing ratio for 41mph.

What happens when I throw another motor in? How does it change my top speed and gearing ratio? Do I keep gearing ratio the same and top speed is still 41mph?
Stats for 6374 SK3 Motor on 10S.
111.060 km/h / 80.4672 km/h = 1.38 That's your gearing ratio for 50mph.
111.060 km/h / 66 km/h = 1.68 That's your gearing ratio for 41mph.
111.060 km/h / 44.2803 km/h = 2.50 That's your gearing ratio for 30mph.
111.060 km/h / 55.5 km/h = 2.00 That's your gearing ratio for 34mph.

On a 10S setup it's much harder to reach higher mph. Does a second motor help to bring up the top end speed? I'm trying to figure out a setup that would allow for 50-60mph. It looks like top speed is 1:1 being the best ratio to 1:1.60 are the best ratios. Meaning you would need for example a 12T and 12T but is that even doable would the start up be a slow and no torque? I assume, this is why 5-10 speed bikes have different gears which you can use for either more torque and/or speed.

The best setup would be a 2.00 gearing ratio 15 Teeth Motor Pulley and 30 Teeth Drive wheel at 1:2 gearing ratio for top speed. A second motor will account for another 30 percent? You could do 20 Teeth and 40 Teeth but it would be more difficult and wouldn't go as fast since it's not the lowest ratio.
Last edited by torqueboards on Sun Dec 01, 2013 11:37 am, edited 2 times in total. View post history.
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Re: Best Pulley Gearing Ratio Eboards?

Postby Miles » Sun Dec 01, 2013 11:47 am

You might find this spreadsheet handy for your calculations:
viewtopic.php?p=312555#p312555

The aerodynamic drag coefficient for a person on a board will probably be somewhere between 1.0 and 1.2.
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Re: Best Pulley Gearing Ratio Eboards?

Postby Miles » Sun Dec 01, 2013 12:00 pm

BTW, it may have been mentioned already but, yes, the Torque Constant (Kt) is the reciprocal of the Velocity Constant (Kv) but only if both constants are defined in SI units (Radians-sec/V and Nm/A) . To use Kv as rpm per Volt, the formula is Kt = 9.549/Kv
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Re: Best Pulley Gearing Ratio Eboards?

Postby whilechukwuzout » Sun Dec 01, 2013 5:30 pm

I think somewhere between 1:4 and 1:5 is ideal. I have 1:3 on my setup and it is capable of speeds far beyond what anyone should be doing on a skateboard. Trading top speed for torque is a good thing. Also keep in mind that the system works best at full throttle, as less energy is dissipated by the ESC.
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Re: Best Pulley Gearing Ratio Eboards?

Postby torqueboards » Sun Dec 01, 2013 6:36 pm

What if your looking to fo 40-50mph? 12s dual motor 6374mm's. Would a 1:2 ratio be better? 20t and 40t? I know you can do 15 teeth and 30 teeth would be better but its harder to fit a 30 teeth pulley unless its custom made. Would extra teeth make a difference for top speed.
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Re: Best Pulley Gearing Ratio Eboards?

Postby lpbug » Mon Dec 02, 2013 3:02 pm

Wait torque, would you ever go that fast? :shock:
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Re: Best Pulley Gearing Ratio Eboards?

Postby Jonboy » Mon Dec 02, 2013 6:44 pm

My trusty steed.. The Raptor 140

viewtopic.php?f=6&t=64029
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Re: Best Pulley Gearing Ratio Eboards?

Postby Murfix » Tue Dec 03, 2013 5:16 am

Miles wrote:BTW, it may have been mentioned already but, yes, the Torque Constant (Kt) is the reciprocal of the Velocity Constant (Kv) but only if both constants are defined in SI units (Radians-sec/V and Nm/A) . To use Kv as rpm per Volt, the formula is Kt = 9.549/Kv

Thanks for freshing that up!

That spreadsheet looks useful. There are a dozen other gear ratio calculators out there if you don't want to do the maths yourself.
Memo to myself: Screw it, just do it!
1 Apr 2013 - Start pre-engineering my first EV build!
6 Aug 2013 - Ordered all parts for my Emtb 8s 2x2kW 270kv Alien ESC setup.
3 Sept 2013 - All parts have arrived: on to the build!
23 Sept 2013 - First test ride: AWESOME!
7 Feb 2014 - Upgrade finished: 3kW motors, 12S Alien ESC, entire new drivetrain and LED's!
Build topic: viewtopic.php?f=35&t=52390
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