These days you can get collars to keep wheels in place on wire undercarriages. They are quick and easy to install but they can easily fall off too. I use thread locker on the grub screws that hold the collars in place.
There is another way. Solder washers on to your undercarriage axle to hold the wheel in place.
I use a brass washer with a hole the same diameter as the undercarriage leg to make a collar that will hold a wheel in place (and won’t fall off). But, how do you stop solder and your soldering iron from damaging the wheel while soldering the washer in place? Even if you are using wheels with a metal hub there’s still a risk of accidentally touching the tyre with the soldering iron. The answer is to use a cardboard protector.
Put a cardboard protector over the wheel.
Solder the washer in place.
Remove the cardboard and hey presto a soldered wheel retainer.
