I just wanted to share my thoughts about lead screws and the like for Z axis motion. I have read numerous posts on various forums by people claiming that threaded rod isn’t accurate or that it is only suitable for holding things together and never for linear motion. They will then go on to say that one should use “proper” lead screws.
So my first observation is that, by definition a lead screw is a threaded rod. However, I don’t really want to enter into this endless debate, except to say that I am comfortable with my own decision to use threaded rods which were not specifically branded as being “lead screws”.
What I do have a bit of a problem with is multi-start lead screws for use on Z axes. It seems that people buy them because they are labelled “lead screw” and therefore must be superior. Many machines are built using them too – probably because the manufacturer thinks they will sell more if they can say they use “lead screws”.
One very important thing to think about is “lead” (pronounced leed not led). This not the same as pitch although often people think that it is the same thing. It happens to be the same thing for single start screws but for multi start screws, it is completely different.
To illustrate the point I have been playing around with OpenScad, wrapping a helix around a cylinder to simulate what a screw thread might look like.
Here are two images of a rod 8mm tall.
The pitch of a screw thread is the distance between two “peaks”. As you can see, there are 4 of these peaks over the length of the 8mm rod in each picture so the pitch is 2mm in both images.
This next image is the same as the top one but looking more from the top.
If you trace a line from the top of the rod and follow it around anticlockwise for 1 full turn, you’ll see that you end up exactly 1 pitch distance (2mm) below where you started. This is the lead and it means if a nut was held on the rod so that it couldn’t rotate, in revolution the nut would move 2mm. This is a 2mm pitch single start screw so also happens to have 2mm lead.
Now let’s look at the top of the second image.
Here we can see that it is completely different and that is because it is a 4 start screw, with each helix offset by 90 degrees. Now what happens if you trace the line as before? To make it easier, I’ve taken away 3 of the threads and left just one……….
………and from the side it looks like this
As you can see, an 8mm single start screw wouldn’t have much contact area between the screw and a nut which is why they are made with 2 or 4 threads offset by either 180 or 90 degrees to each other.
So now we can see that tracing a line for 360 degrees as before moves us the full length of the rod (8mm) so the lead is 8mm. This is a 2mm pitch 4 start lead screw and people buy them because they think that 1 revolution will mean a linear movement of 2mm when in fact 1 revolution will give 8mm of linear movement.
Why is this not a good idea for our Z axis? Firstly look again at the angle of the helix and compare it with the top picture which is a single start screw. You’ll see that it is much steeper. Therefore, a heavy Z axis bearing directly down on the rod could exert enough force such that the bed would fall under it’s own weight as soon as power to the motor is lost. Also, it will require more torque to drive the rod because it has to move the load a greater distance for a given angular movement (in the case 4 times greater). So we’ll most likely need a bigger motor.
But most importantly it will have an adverse effect on accuracy, which is ironic when people buy lead screws because accuracy is their main criteria.
To elaborate on this, I need to do a little maths. An average stepper motor moves 1.8 degrees between steps (I am aware that one can buy 0.9 degree stepper motors but they are more expensive). So, I revolution will be 200 steps assuming we have 1:1 gearing and are not using asymmetric pulley sizes. For our 2mm single start screw which has a lead of 2mm we can say that 200 steps = 1 revolution = 2mm. Or it’s 100 steps per mm which means that for a resolution of 0.1mm layer height, it will be 10 steps, 0.2mm will be 20 step, 0.3will be 30 steps etc.
Now for the 4 start, 2 mm pitch lead screw which has a lead of 8mm, 200 steps = 1 revolution = 8mm. So instead of 100 steps per mm we now have 25 steps per mm and for our 0.1mm resolution we have 2.5 steps, for 0.2mm it’s 5 steps and for 3mm it’s 7.5 steps. Which means we will be relying on micro stepping for positional accuracy for anything other than our 0.2mm layer height. And micro stepping does not improve accuracy. In general, stepper motors are quoted as having a non accumulative positional error of +-5% which for a 2mm lead screw, equates to about 0.01 mm but for an 8mm lead it becomes 0.04mm which may start to become significant with 0.1mm resolution layer height.
So, multi start lead screws are designed to give a large linear movement for a given angular movement. They require more torque to drive them and provide less holding power than a single start screw of the same pitch. Basically designed for speed which would be fine for our X and Y axes but not what we want for our Z axis.
In my opinion 2 start, 2mm pitch screws are just about acceptable or 4 start but with 1:2 gearing. Finally, this is an image representing what I use.
It’s 8mm diameter, 1mm pitch single start trapezoidal threaded rod. It gives me 20 full steps per 0.1mm and requires very little torque enabling me to use 3 of them to lift my 7.3 kg bed with a single Nema 17 stepper motor. If you look at my other posts, you’ll see that I can print 300mm x 300mm with no bed compensation (despite the fact that these screws didn’t have the “lead screw” label) so I’m happy with the accuracy. Maybe they will only last 30 years instead of 50 but who cares – they are cheap enough to replace (much cheaper then “lead screws”).
That was just my twopence worth……….