Ball Screw Selection and Preload Specification for Positioning Axes
A positioning axis has been running with visible pitch error and a faint hammering every time it reverses direction. The repeat pass lands 0.03 mm off. The maintenance log blames the coupling; the operator blames the motors. Neither is right. The real offender is an undersized ball screw running with zero preload, ordered three years ago because somebody divided the catalogue load rating by a safety factor and called it done. Screw selection looks simple until you put numbers on it.
What the Load Case Actually Looks Like
Most machine axes do not push a constant force. They accelerate a table, cut or move a load, then decelerate. The screw sees the axial component of all of these. A selection done on peak load alone will almost always end up oversized on days one and undersized on year two, because fatigue, not peak load, kills ball screws.
Start by writing the duty cycle in seconds. A typical feed axis runs like this: accelerate in 0.15 s, run at constant speed for 1.2 s, decelerate in 0.15 s, dwell for 0.5 s, then cycle. For each phase you need the actual axial load, not the nameplate number. During acceleration, inertia dominates; during steady run, friction dominates; during cutting, process force dominates. Most suppliers publish a mean load formula that weights each phase by time, and if you skip that step you are sizing the screw for a load profile that does not exist in your machine.
A worked example keeps this honest. Table and workpiece mass 220 kg, target feed force at speed 1.4 kN, coefficient of friction on the guideways 0.05. Friction alone is about 110 N acting against motion regardless of direction. Add acceleration force from the table inertia reflected to the screw: with a pitch of 10 mm and a motor inertia ratio around 4, the reflected inertia contribution can reach 400 to 600 N during a 0.15 s accel window. Add process force. The screw that survives this machine is the one sized for the fattest combination, not the arithmetic mean.
Diameter, Lead and the Real Constraint
Two parameters do most of the work: lead and diameter. Lead sets speed and resolution; diameter sets stiffness and critical speed. A common mistake is choosing a generous lead like 20 mm to get speed, then discovering that the servo encoder resolution maps to a poor linear resolution, or that the screw cannot be run at rated speed because its critical speed limit, which depends on the unsupported length, is lower than the motor speed.
For speed, the relationship is linear: axis speed equals lead times rotational speed. For a 30 m/min axis and a 20 mm lead, you need 1500 rpm at the screw, which is fine. But if the axis is 1.8 m long and supported only at both ends, the fourth power dependency of critical speed on length often forces a larger diameter than the load maths requires. Designers who ignore critical speed end up chasing vibration that no amount of motor tuning will remove.
Stiffness gets the same treatment. The axial stiffness of a ball screw is dominated by its root diameter, not the ball diameter. Two screws with identical leads but root diameters of 18 mm and 24 mm differ noticeably in deflection under load. For a positioning axis that must hold position under load, the root diameter, the nut mounting, and the bearing arrangement together define how much the screw stretches. Plan for the nut to sit on a stiff, machined face and the drive bearing on the side that sees the cutting force. Flipping this arrangement saves money on paper and costs accuracy on the floor.
Preload Is a Behavioural Choice, Not a Catalogue Option
Preload controls one thing above all: whether the nut has measurable axial play when the direction reverses. A nut with zero preload has play that shows up as lost motion, which shows up in the parts as a reversal bump. Preload removes that play by putting the ball circuit under internal compression so that load reversal never crosses a zero-force gap.
The engineering trade is stiffness against life and heat. A preloaded nut is stiffer, but it runs warmer and sheds life because the rolling elements carry a constant preload load on top of the working load. Catalogue values tell you the internal preload as a percentage of the dynamic load rating, and the rules of thumb are simple: light preload for long-stroke inspection and measurement axes where heat is poison, heavier preload where the axis both positions and carries cutting load, and no preload at all only where reversal accuracy is irrelevant and the cycle is short.
For the axis in our example, the right answer is a medium preload class. It removes the reversal error entirely when paired with backlash-free double-nut mounting, while keeping temperature rise under a degree or two at the operating speed. When the motor reverses, the move starts instantly rather than after the nut lugs travel across their internal clearance. That one catalogue choice was worth more than the motor upgrade the operator kept requesting.
Life Calculation, Done With Real Numbers
The catalogue life formula is a power law: rated life is proportional to the cube of the rated load divided by the actual mean load, for ball screws, with a documented life under the rated dynamic load. Put real numbers in. Take a 32 mm screw with a dynamic load rating around 20 kN. Run the duty-cycle weighted mean load at 4 kN and the life formula gives something near 100 times the rated life. Run the same screw at 12 kN nominal and the exponent works brutally against you: life collapses to a few years of single-shift work. This is the entire reason load profiling matters. A design team that used the arithmetic average of the loads shipped a screw that needed replacement after eighteen months; the same screw with a correct mean load estimate runs past its fifth year.
Count turns per unit distance into the calculation as well. A feed axis that reverses ten times a minute wears the balls differently than one that dwells after every stroke. Recent experience-based guidance from several screw suppliers flags stroke length and cycle frequency as the two inputs most often wrong in customer life worksheets. If an application reverses every few seconds across the same 300 mm stretch, the balls travel a long total distance per shift and the wear concentrates on a narrow band of the nut raceway. Budget the life accordingly.
End Play Versus Preload: The Zero Backlash Illusion
Engineers sometimes think buying a “zero backlash” nut removes the need to think about preload. It does not. Zero backlash at the catalogue bench is measured when the nut is new, on a fresh screw, under a fixed measuring force. In service the nut carries working load oscillations, temperature swings, and ball wear, all of which change the running clearance. A nominally zero-backlash nut that was not set up with deliberate internal compression becomes, within a year, a loose nut with visible reversal error. The preload value is what keeps the ball pack under compression throughout that service life, and choosing it consciously is what separates a controlled axis from a lucky one.
There is a direct relationship between preload and the drag torque the motor must overcome. Every N of preload appears as additional friction torque on the motor shaft, so the sizing calculation should add preload torque to the friction and acceleration components rather than pretending the screw is frictionless. A nut with heavy preload can add 20 to 40 percent to the required motor torque at low speed. When a designer discovers the motor is marginal, the first thing to re-examine is whether the preload class was chosen a step too heavy for the duty cycle, not whether the motor needs a frame size up.
Measuring What You Actually Bought
Catalogue preload classes are useful until the box arrives. Before the nut goes on the machine, check the measured drag torque against the range the supplier prints for that preload class. A combination torque wrench reading on the screw while rotating a stationary, greased nut at low speed gives a sanity figure for the preload torque component. More useful still is a dial-indicator back-to-back reversal check after mounting: fix an indicator on the table, command a slow approach in both directions, and read the lost motion at the point of reversal. Fewer than about 5 micrometres of lost motion at the table, for a mid-size feed axis, indicates a healthy preload setup. Digits two or three times that point to preload loss, a worn ball track, or a compliant mount, and it is worth finding before first part, not after the third shift.
When a Roller Screw Is the Right Escalation
Ball screws have their ceiling. For stroke where the nut must also take bending or where mean loads are sustained and heavy, a planetary roller screw moves the raceway from point contacts to line contacts and multiplies both load capacity and life at the cost of price and lead time. The selection logic does not change: the same duty-cycle mean load method applies, and the roller screw simply shifts the life curve upward. Applications that hammer a ball screw into early replacement — presses driven directly, actuators that hold load with the brake closed, axes with frequent high-load reversals — are the candidates. If the numeric life calculation on a ball screw comes back under about two years of the target shift count, run the same numbers on a roller screw before accepting a compromise in size.
Cooling and the Temperature Budget
A preloaded screw running through a long duty cycle generates heat in the nut and in the bearings. On an axis with a heavy preload and frequent reversals, the screw can grow axially by tens of micrometres from nut heating if it is rigidly anchored at both ends. The classic answer is the fixed-floating arrangement already described: locate the thrust bearing at one end as the datum and let the other end float. But the datum end itself must not wander. A machine that references position from the motor feedback loses accuracy exactly when the screw grows; a machine that references from a glass scale or from the table position stays honest because the feedback sees the table, not the screw. Deciding early whether the axis is screw-referenced or scale-referenced changes both the bearing strategy and the preload budget.
Verify the temperature budget the same way you verify speed. At the design review, ask what the screw temperature rise is at the worst cycle and how many micrometres of axial growth that implies at the datum end. If the answer is “we do not know,” the review has found its action item before a single part is machined.
Tolerances on the Mounting Features
The ball screw does not run any more accurately than the parts it is bolted to. The housing bore for the drive bearing should carry a concentricity callout relative to the axis datum, the nut mounting face should be perpendicular to the screw axis within a few hundredths of a millimetre, and the screw axis itself should be aligned to the guideway within about 0.05 mm over the stroke for a machine of ordinary precision. Tolerances tighter than the process can hold add cost without adding performance, because the screw aligns itself to the guide rails through the nut only when alignment errors are small. A practical specification is to call the bearing seat concentric within 0.02 mm and the nut face square within 0.05 mm per 300 mm of travel, then verify with a clock gauge during mounting.
Verdict for the Hammering Axis
The axis that reversed with a bump and drifted 0.03 mm was not saved by a better motor. A catalogued 32 mm, lead-20 mm, medium-preload screw with a fixed-floating bearing arrangement, a stiff disc coupling, and a duty-cycle life calculation came back with a mean load under half the rated load, a predicted life past the machine’s planned service interval, and an expected reversal error well under the positioning tolerance. The parts list changed by maybe fifteen percent of the axis cost. The behaviour of the machine changed entirely. That is the whole argument for treating ball screw selection as an engineering exercise with real numbers instead of a catalogue lookup.
