BallSCREW
There are two distincttypes of ball screws:
1) Rolled
2) Ground
Ground ball screws are found in accuracy grades C0 to C5 with C0 being most precise.
Preload
A preload is provided in order to eliminate the axial clearance and minimize the displacement under an axial load. For a highly accurate positioning, a preload is necessary. The rigidity of the nut is increased.
There are different types of preloads, the most used are the preload through oversized balls. The second way is to achieve the preload with a double nut and a spaced between them or with offset preload. Note that an excessive preload adversely affects the service life and heat generation.
My choice
My goal is to get a precision milling machine so the choice between rolled and ground was quite easy. Grounded with accuracy grade C3 would be perfect. The question was what diameter, what pitch, and what type of preload.
Concerning the preload. After some research on internet, I discovered that the recommendation for smaller strokes and smaller cutting forces is oversized balls. In any other cases, the double nut should be preferred. Therefore I selected preload with oversized balls.
Pitch and diameter. At the beginning I was biased to go with 16mm diameter with pitch of 5 mm, similarly as it is found on Chinese CNC milling machine 3020 etc. I was considering stepper motors with 200 steps per turn, so this would give me precision of 5 / 200 = 0.025 mm. This was somewhat more than I wanted at the beginning, so I started slowly to think about a smaller pitch. Clearly, my machine will be mostly for small parts of robots, gears, joints, etc., so I don't need any fast long movements. I though 120 mm/sec would be more than sufficient. With 2000 rpm I would need pitch of about 4 mm. I found ball screws from TBI with this pitch. I checked some catalogues for milling ends for plastic and wood materials with diameter of 1 mm to 3 mm (probably the size I will use at most), and the cutting speeds are about 4.5 m/min (75 mm/s) at max with spindle speed of 60000 RPM. Then, I maybe don't need 120 mm/sec and less would be sufficient. It took me a while of thinking and I decided that I'll go with 2 mm pitch (66 mm/s). 0.01 mm precision with stepper motor. I dropped also an idea having diameter of 16 mm since it looks that for strokes less than 25 cm it was unnecessary big. During motor sizing I found that diameter of the shaft has a quite large impact on the motor size due to the screw moment of inertia.
All this decisions has been accompanied with the sizing calculations I typed in Mathcad. The selection of screws and motors was an iterative process which took me truly quite a time. Looking backwards, I should made a table with pros and cons for each case and I would probably end up with the same decision in a fraction of time. The Mathcad file for the sizing is here.
I wanted buy all screws from TBI, since they have reasonable prices. Unfortunately, it seems that type xx with 2 mm pitch found in the catalogue is not produced with oversized balls. I tried ebay and was lucky with used NSK screws with pitch 2.5 mm (83 mm/sec at 2000 RPM). For Z axis I bought also a used ball screw from THK, MDK-1202-3 type with a pitch of 2 mm - no preload, axial clearance > 0.005 mm.
The screws I bought were to long . Therefore, I unscrewed the nuts and give the screws to a friend who was willing to finish the shaft ends on the grinding machine. How to unscrew the nut? Easily. Prepare a plastic tube with the outside diameter a little bit smaller than the screw shaft root diameter and with the inside diameter larger than the end shaft diameter. In my case for 12 mm screw diameter, the screw shaft root diameter is 10.9 mm and the shaft end 8 mm. My plastic tube has ID of 8.2 mm and OD of 10.8 mm, length xx mm. The photos are below.
Note: The end shaft fixed support should be tightened with a given torque. The values are provided in the NSK catalogue on page B382. For my support unit WBK10-01A, the locknut should be tightened with torque of 280 N-cm. Set screw (M4) with a torque of 147 N-cm.
X, Y axis
12 mm diameter
2.5 mm pitch
total length 330 mm (max. stroke 221 mm) for X-axis and 280 mm (max. stroke 171 mm) for Y-axis.
NSK W1202MA-7PY-3CZ2.5, price xx + TAX/duty xx =
Z-axis
The input to calculation:
The mass of gantry is given by
- 2x sliders (HiWin HGH20CA), 0.6 kg
- nut + nut holder, 1.0 kg
- plate, 1.1 kg
- arm, 1.6 kg
- spindle holder, 0.1 kg
- spindle, 1.4 kg (Kress 800 maximum)
In total 5.8 kg.
I found that high efficiency of the ball screw tends to let the ball screw back drive under load (i.e. converting linear motion to rotary motion). This is especially true on the vertical axis where the weight of gantry can overcome the friction forces and can actually move downward if no break or some sort of counterweight is applied.
The back-drive torque is given by the formula:
Tb=(Fg*P*n2)/(2*pi) = (60*0.002*0.9)/6.28 = 0.02 N-m.
where, Fg is the weight (in newton's), P is screw lead (in meters), n2 is back-drive efficiency. Note that n2 is a function of lead angle and it is slightly smaller than efficiency for normal operation (check the datasheet).
The friction torque consist of:
- starting friction torque of nut (break away torque)
- end seals
- end bearings
Unfortunately, in contrary to my X and Y ball screws, I have no idea what my THK Z-axis ball screw type is and what are the bearings and the end seals. Therefore I decided to determine the back-drive torque experimentally. I attached the supports on the wood board and the nut subjected to a force given by the mass of hanging weight. The screw started to turn with mass of xx kg, i.e. torque of xx N-m. This would mean that static friction torque is xx N-m. I found that the dynamic friction torque is about xx times smaller than the static one, i.e. xx N-m.
Z-axis: Tstatic = xx N-mm, Tdynamic = xx N-mm
I made a similar test for X and Y ball screws with the following results:
X-axis: Tstatic = xx N-mm, Tdynamic = xx N-mm
Y-axis: Tstatic = xx N-mm, Tdynamic = xx N-mm
Counterweight
There are two options. The first is to use a pulley style counterweight. The second would be a constant force spring.
1) Pully counterweight - advantage is that this does not need any maintenance and will last forever. Disadvantage is that counterweight adds an inertia and some spring stiffness to the sail. This in turns could lead to a oscillations at fast accelerations and decelerations.
2) Constant force spring - advantage is that this spring generates constant force without inertia effects and oscillations. Disadvantage is that the spring experience a material fatigue.
After some thought I decided to go with the constant force spring:
- Initial deflection to reach rated load = 1.25 * OD.
- The drum diameter should be 10 to 20% larger than its natural diameter.
- One and one-half wraps should remain on the drum at maximum extension.
I bought two xx from sodemann-federn.de.