A gantry axis drifted 0.05 mm when the load pushed against it. The screw was 32 mm diameter, 10 mm lead, 1200 mm between bearings. The mounting was fixed-supported: a pair of angular contact bearings at the drive end, a single bearing at the far end. Under the 2000 N axial load, the screw deflected between the fixed bearing and the support. The axis lost its position every time the load reversed. The fix wasn’t a bigger motor or a tighter servo loop. It was a fixed-fixed mounting.
The four arrangements
Fixed-fixed. Bearings at both ends, each end located axially. Highest stiffness, handles thermal growth with a preloaded bearing pair at one end and a floating pair at the other. Standard for precision axes.
Fixed-supported. One end fixed (axial lock), the other simply supported (radial only, axial float). Simpler, cheaper, but the screw deflects between the ends under axial load.
Fixed-free. One end fixed, the other free. Only for short, light axes.
Supported-supported. Both ends float radially. Lowest stiffness. Only for very short travel.
The gantry axis used fixed-supported because it was cheaper and the travel was only 1200 mm. The deflection under 2000 N was the problem.
The deflection math
A ball screw under axial load behaves like a column. The axial stretch under pure compression is delta = F x L / (E x A). For the 32 mm screw: A = pi/4 x 0.032^2 = 8.04e-4 m^2. E = 210 GPa. delta = 2000 x 1.2 / (210e9 x 8.04e-4) = 2400 / 1.69e8 = 1.4e-5 m = 0.014 mm.
That’s the pure stretch. On top of it come the bearing deflection at the fixed end and the nut-to-bearing clearance. The customer measured about 0.05 mm total. The stretch was a third of it. The rest was bearing deflection and the support end’s compliance.
With fixed-fixed mounting, the same load stretches the screw from both ends and the effective length halves. The stretch drops to 0.007 mm. The bearing deflection stays, but the total drops below 0.02 mm. The gantry regained its repeatability.
The bearing choice at the fixed end
The fixed end needs a pair of angular contact bearings, back-to-back, preloaded. The preload removes the axial clearance so the screw doesn’t shift under load reversal. A single deep-groove bearing at the fixed end has axial clearance. The screw moves the clearance distance before the load picks up. That’s lost motion.
The support end, in a fixed-fixed arrangement, uses a second bearing pair with axial float. The outer race is loose in the housing. It carries radial load and lets the screw grow thermally without preloading the first pair into the housing.
Thermal growth: the 12 microns per degree rule
A steel screw grows about 12 microns per degree C per meter. A 1.2 m screw heating up 10C grows 0.14 mm. In a fixed-fixed mounting, that growth must go somewhere. The floating end lets it expand axially. If both ends are locked rigidly, a common mistake, the screw buckles or the bearings overload. The floating bearing at the far end is what makes fixed-fixed work.
On the gantry, the screw warmed up 8C during a two-hour run. The floating end absorbed the 0.11 mm growth. The axis held position. Before the fix, the fixed-supported arrangement let the growth push the screw against the support bearing. The preload changed with temperature, and the axis drifted 0.02 mm per hour.
Critical speed and the nut
A long screw has a critical speed, the rotation speed where it whips. For a 32 mm screw with a 1200 mm span, supported-fixed, the critical speed is around 3000 rpm. The gantry ran at 1500 rpm, so it was safe. But if the axis needed 4000 rpm, the only fix is a larger screw or a fixed-fixed mounting, which raises the critical speed by about 20%. The mounting arrangement isn’t just about stiffness. It sets the speed ceiling too.
Fixed-supported is fine for short, light axes. The 1200 mm gantry under 2000 N needed fixed-fixed. The 0.05 mm drift wasn’t a servo problem. The screw stretched and the support bearings deflected. Add the second fixed bearing pair, let one end float for thermal growth, and the axis holds where it’s told.
