Was about to get a toy- then I did some research...

[JAZZCNC]

Andy I'm quoting you but please don't think I'm having a pop at you or knocking what you said. I mostly using the quotes to point other factors out and clear some things up.

A 1605 or 1610 screw will have a root diameter of ~12mm. Using a BK BF setup, a 1000mm screw can get to around 1500rpm before whipping is an issue. That limits our rapids to 7.5m/min on a 1605, or 15m/min on 1610..

Ok well forget this because it's not that simple, there's too many factors involved which make these calculators of much use to a real-world DIY machine. I've built machines that use 16mm dia 10mm pitch screws at 1100mm that will happily reach 25+Mtr/min without whipping. How they are aligned and ball-nut mount fixturing etc all kick in and screw these calculations up. Similair is true of the Motor calcs as well, I've seen them things spit out stupid numbers.

Typical stepper motors will be falling off in torque dramatically above 1000rpm = 5m/min 1605 or 10m/min 1610. This is where your belts come in, its about allowing the motor to stay at appropriate RPMs for the speed (or torque multiplication).

Belts can be used for this reason but it's not the main reason why I use them.
There are two main reasons why I use belts.
#1 Is to allow me to use a higher pitch screw and apply a 2:1 ratio which then lowers the screw speed by half so whip is lowered. Torque is doubled due to ratio but is offset because the linear torque of higher pitch is lower, one cancels the other in effect. I mostly use this approach on longer machines.

#2 Is to lower the affects of resonance on the motors/drives. This gives a much smoother running motor and often allows higher RPM because the drives are not having to deal with resonance issues. Don't underestimate resonance and how it can affect a stepper motor, it can literally cripple a motor and half it's RPM.

Now, I'd personally aim for rapids in the 7.5-10m/min range for a wood router, which suggests 10mm pitch screws, but some people are happy with the 5m/min.

Now, this is where it gets sticky and motor/screw selection becomes very important.
For a balanced machine your better to size motors and screws not for rapid speed but in such a way that your cutting with the motors at an RPM that gives good torque while cutting.
Ideally, you'd use the Motor Torque/speed curve graph to help select the right screw pitch to give the feeds your most likely to cut at for the materials your cutting mostly. But most Stepper manufacturers are about as trustworthy as politicians so you can't believe any of the bull shit they show. Plus lots of other factors come into play like voltage they are being run at and how wired etc.

So we know through experience that a typical NEMA 23 motor wired in parallel with voltage in the 60-70v region above 1000rpm torque starts to drops off and above 1200rpm drops quickly to about 1500rpm then stalls can occur.

Now for a router cutting mostly soft materials or man-made boards using a carbide cutter and extraction for chips, will be between 6-10 Mtr/min. Now the higher end won't work with a 10mm pitch because the motor would be spinning at 1000rpm where torque is low and dropping away. So we need a higher pitch or motors that spin faster with torque ie: servos.
So keeping with steppers then we need to change the pitch, the next common pitch would be 16mm. This gives 10,400mm/min at 650Rpm which is a little too low rpm at this speed, 750rpm would be a nicer figure but this gives 12,000mm/min. So here's where a small ratio on the belts would kick in and allow us to balance the machine up. Reclaim a little linear torque and lower screw speed. Plus the added advantage of better resonance handling.

So a 1.25:1 ratio would be like a 12.8mm pitch which at 750rpm would give 9600mm/min which is a nice area with good amount of torque. With rapids in the 15Mtr/min range at 1200Rpm and without getting too close to the stall point, which on a stepper at 70vdc is around 1300-1500rpm dependant on alignment etc. However, because of the ratio, the screw speed would be around 960Rpm so we are still ok regards whip. We have also gained back a little torque from the ratio.

So it's winner, winner chicken dinner and we have a nice balanced machine. That will fly like the wind and cut at correct feed rates with good amount of torque left.

However at DIY level most don't cut correctly or with carbide tooling or chip extraction so they manage with 10mm pitch and just cut slower. However, if they ever decide to cut correctly or with carbide tooling etc then they will struggle or fail. The balanced machine above will cover all bases with only real loss being slightly less resolution.

As for the Z axis, the travel is massively reduced so large rapids arn't an issue. A finer pitch should give slightly higher accuracy and holding torque at the correct Z location, so I'm all for fine pitch Z screws. 1605 should be fine.

Those motors sound a little weak to me. You should use the motor calculation sheet to determine what you need. Mines a similar size, and I use 2x2010 X screws (2x4nm low-inductance nema23 steppers) and a 1610 Y screw (3.1nm).

Spot on, on both accounts, except using the motor calculator. The key to speed is low inductance motors with plenty of volts wired in parallel.