You should really know the helix angle of the gears, otherwise it is just guessing - e.g. with a 15deg helix angle your existing gears should be 111.8 and 173.9mm respectively.

I measured the angle the best I could and it is 10 deg

Occupant

How did you came up with those numbers?

Several years ago I wrote a program to calculate all these values, but you could try to get a catalog from Quality Transmission Components "Handbook of Metric Gears" that includes calculation formulas. However, if you stick with a 15deg. helix angle, the values should be 20 teeth -> 91.1, 22 teeth ->99.4 and 24 teeth 107.7 all with a module of 4mm. and that is also assuming no modifications from standard gears such as profile shift.

Thanks Occupant. But the helix angle is 10deg. Please give me the values for 10deg

Although I slightly disagree with Occupant's results I totally agree with Occupant when he says "You should really know the helix angle of the gears, otherwise it is just guessing". If you stick with the angle being 10deg this would make the 40 & 25 tooth gears non standard with a correction approx 3mm & 1.5mm also what Module are you going to cut them, it is possible that they are 4 Module??.Here is a quick way of calculating your sizes. (Teeth x Module / Cosine of the Angle) this is your PCD to this add (2 x addendum)if you use this you will see why Occupant arrives at 15 deg.

I have measured again using a different technic and YES the helix angle is 15deg! 100% sure
I also drawn the shape of the teeth. See attached file

In my humble opinion, it is not so easy to measure the helix angle with reasonable accuracy, as a 0,02 mm error will ruin the contact pattern, and assuming the gear is 20 mm thick I calculate 0 degrees and 3 minutes. The helix angle is by definition measured on a pitch diameter, which depends on module and this angle itself. There is no reason to believe, that these gears are not profile shifted. If the goal is to correctly identify the gears and manufacture a set of good replacements, then it is not a trivial task at all. It's a long story, which gets longer as being told, and I don't want to be boring, but I hope I have provided some important information for you to decide what to do next.

spigor
The gear thickness is 40mm. They are from a very old wire drawing machine (around 1950s) and yes I need new pinions and I dont have any other information about the gears except those samples which are originals
Could you explain what is a "profile shifted gear"?

As you said: The goal is to correctly identify the gears and manufacture a set of good replacement. I know that probably the best approach should be to send the gears to a gear shop and ask them to manufacture the pinions accordingly by just telling the number of teeth that I need but there are no good gear shops around here and I personally dont trust them at all

If the thickness is 40 mm, then the error gets down to just under 2 minutes.
By "profile shifted gears" I mean gears with addendum modifications.
Let us know how we can help you further.

thanks spigor

We are starting to machine the gears today. Material is steel grade SAE 8620 and they will be case hardened after they are finished
I am using Occupant`s diameters