I've removed a number of cranks from bikes built in the mid 1990s and later with my inexpensive crank-pulling tool, but I have been unable to remove the drive-side crank from a 1980s-era bicycle. The NDS came off with a little coaxing. No luck on the drive side. The steel of the BB spindle is harder than the metal of the crank pulling tool and is chewing it up. I'm open to suggestions. Are vintage versions of these tools made of stronger metal?
You can get these tools with a rotating contact part. The park tool does this amongst others. You have to be willing to invest a little more but the tool is more capable.
You could try supplying a small disc of hard metal at the contact point if you can find anything of a useful size, it may or may not help with your particular tool.
If you are removing the crank in order to dispose of it, there are some alternatives. Please clarify whether that's the case.
Let us imagine that you stick with your old tool or the threads in the crank get destroyed. You still need to remove the crank and it's a sacrificial part in this case.
If the crank is aluminium/alloy, it's easy enough to cut accross the hole where the crank bolt goes, as deeply as possible and with a view to being easily able to smack parts of the crankset with a heavy hammer. You can't cut through the bottom bracket axle because it is made from a metal that is harder than your hacksaw blade, so don't worry about that. Protect the frame where necessary and support it approprately from the other side on the floor to take up the shock. You can either beat the crankset gently, expanding your cut, perhaps with a wide/thick screwdriver blade as a chisel, and alternately knocking it offwards until you have success or you can give it hell and beat it hard until it breaks where you have weakened it with the cut. This technique doesn't work for steel cranks but it's very theraputic and gives your workshop a priceless "no shits given" atmosphere.
Grease the end of the puller and threads. The idea is to remove as much friction as possible to maximize pulling force (although looking at your puller, you don't seem to have had a problem generating significant force).
Presuming aluminum cranks, as aluminum expands more than steel, heating the crank arm should help. Try a little heat first then add more. Take care not to over heat the frame, you want the heat focused on the aluminum of the crank.
A bit of percussion with the pressure from the tool can help. Best to have the crank arm supported underneath and hit the top, so minimal forces got though the BB and into the frame.
One very often success technique is loosen the retaining bolt (But leave it in place to stop the crank arm falling off) and go for a ride. The crank arm will often loosen. If you do this, consider it a destructive technique for the crank arm, but the BB is saved.
Instead of hacksawing the crank, you can often drill a line of small holes. No need to go all the way though. The idea is you remove enough metal the remain amount will easily yield against the tool. If you do this on diagonal corners of the square, you can then place a punch (or thin screw driver) into the holes and 'open' the crank with a hammer blow (Again, support underneath so the percussion does not get taken by the BB and frame )
Instead of the internal puller, we used a universal external puller.
Something like this (I've no affiliation with Gedore, it was just the picture which came up first): Source
Problem is getting one large enough to fit around the crank. Best case is when the gears can be removed, but with a crank that old, I doubt it.
We opened the retaining bolt just a tiny bit and left it in the BB and used that as the counterpart for the puller (as they likely don't fit into the hole of the crank). We didn't have any damaged threads after this, so the BB should be fine.
If you have to pull at the gears, they'll likely bend and make the crank unusable. Position it in a way so that it'll pull at the position of the mounting points of the gears.