# Wyvern – Ball Screws – Day 5

So it turns out that 1500mm is a magic length for home made CNC machines, who could have guessed. My new super long 1800mm design is going to cause me some problems and I have to decide whether it’s worth pressing on with this design or dropping back down to 1500mm.

The problem is that as the screw is turned there is a tendency for it to deflect out at the centre. As you rotate the screw faster it deflects more and eventually something, probably a bearing, will fail. The longer the screw is the worse this problem is. The magic speed above which the screw is considered to be deflecting too much is called the critical speed. The result is that the longer the screw is the slower it has to be turned which, in this case, means that the gantry moves more slowly.

The problem I have is that the screws mostly commonly used, RM1610, have a critical speed such that at around 1500mm the gantry is moving about as slowly as you would want it to move. I could certainly make the screws longer and still use them but it would compromise the X-axis speed.

There are three solutions to this problem and all have their drawbacks.

# Go Large!

The first solution is to fit screws with a larger diameter such as RM2510. This looks like the best solution as it’s certainly simple to impliment and the apparent additional cost is tiny but it has a massive drawback. The moment of inertia of a rotating shaft is proportional to the radius raised to the forth power. What this means in real life is that a 25mm diameter shaft requires almost six times as much power as a 16mm diameter shaft to get the same performance! e.g. (25/16)4=5.96

The compromise with this solution is that you need a much larger motor to get the same level of performance and the larger motors are more expensive and require more expensive drivers.

# Go Fast!

The second solution is to fit screws with faster threads (or perhaps double starting) such as an RM2020 or RM1616. Taking the RM2020 as an example (because it’s simpler) you would only need to rotate the screw at half the speed of an RM1610 to achieve the same gantry movement speed.

The compromise with this solution is that you lose some positional precision. The stepper motor has a finite resolution and by doubling the screw pitch you effectively halve the resolution you can achieve. This can, to some extent, be recovered by using a 2:1 belt drive and upping the speed of the stepper but then you need larger steppers because the torque drops off on the stepper as the speed increase.

# Go Complex!

The third solution is the hold the screw fixed and instead rotate the ball nut. This is a big advantage because the ball nut is small (length wise) compared to the screw so even a fairly small motor can turn it very quickly. Commercially this is what you would use.

The compromise with this solution should be clear – it’s a lot more complex than rotating the screw. For 1800mm it’s still possible, with sufficiently large motors, to rotate the screw and get good performance so while I like this idea I’m not sure it’s for me.