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Just how much leeway you have will vary from one tool to the next. I have a 14.4v cordless drill with dead NiCad batteries, so I thought I'd try powering it with an 18v lithium pack. The motor works fine at 18 to 20 volts, but the PWM power switch circuit burned out. I replaced it with a switch from another 18v drill with a smaller motor and now it works great. So if you try a higher voltage, be prepared just in case something in the electronics does burn out.
Concrete Metal Lathe
COBRA Naval Base Playset (made with upcycled plastic waste)
Belt Sander Stand
Rain or Shine Solar Charger
Raygun - Steampunk Defense
The Microwave digital timmer hack.
Ultimate Parts Storage