Kids tractor lithium ion conversion

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My kids have a Peg Perego John Deere Gator tractor that uses a 12v battery.
https://www.amazon.com/dp/B000G0KT6Y/?tag=pfamazon01-20

The battery requires monthly charging or it will die. The charge is slow and the winter months are a hassle. I could replace the battery but I'd rather convert it to run on my 18v Makita LXT Lithium Ion batteries.

My tenative plan is to "gut" a Makita LXT flashlight to use the base to clip the battery in, then mod the flashlight base either into the old battery housing or simply with the old battery's pigtail on it. Inside I'd like to have some kind of voltage regulator or other means to convert the 18v output from the battery into 12v for the tractor motor.

The standard battery is a 12v 7Ah lead acid battery and cross references to an Interstate SLA3041
http://www.apexbattery.com/peg-perego-john-deere-gator-battery-sealed-lead-acid-batteries-peg-perego-batteries.html

The Makita batteries I want to use are 18v 3Ah Lithium Ion model BL1830
http://www.makita.com/prod_lxt_battery.htm

I found this DC-DC converter online, but it is expensive and I don't know if it will work: http://www.newark.com/jsp/search/productdetail.jsp?SKU=71K9635&CMP=AFC-TL10000001

This project was inspired by this video from DPX systems who made a mini bike that runs on a Dewalt 18v drill.
http://youtube.com/watch?v=y8abvlYHK3Q


Is what I'm trying to do feasible?
 
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In principal yes, but...

I think the similar toy my kids had averaged about 5 amps and the converter you show is only good for a max of 3 amps or so. Note that peak currents can easily double the average currents.

The drill power pack you show will give about half the runtime of the original battery even if you solve the converter problem.
 
Thanks for the reply. I would be ok with the battery not lasting as long - I have multiple batteries and they recharge in 15 minutes, so I could perpetually keep them going pretty easily.

My electrical knowledge is very limited. I'm a Systems Admin and work on computer systems every, but what goes on inside the power supply unit because it's mostly magic to me. :)

Could I make or get a different converter that operates at higher amps?
 
You would be better off looking into switch mode motor controllers.
Like the one that gives a battery portable drill variable speed.
DC-DC converters are not a good choice for this application.
Finding a 12v LI battery also comes to mind.

Why not just get a timer and set it to charge the existing battery for 15 minutes a day.
Likely much better for the battery than a once a month charge.