Ball Screw

What a ball screw actually is

A ball screw looks, at a glance, like an ordinary threaded rod with a chunky nut on it. The difference is hidden in the groove. Where a plain screw's nut threads slide directly on the screw's threads, a ball screw replaces the threads with a precision-ground raceway — a smooth helical groove — and fills the gap between screw and nut with dozens of hardened-steel balls. As the screw turns, the balls roll in the groove and the nut walks along the shaft, advancing one lead per revolution.

That one substitution — rolling balls instead of sliding threads — changes everything downstream. Sliding friction, the enemy of every plain screw, is replaced by rolling friction, which is one or two orders of magnitude smaller. A plain Acme lead screw dumps half its input torque into heat; a ball screw delivers 90 to 95 percent of it as useful thrust. The balls don't stay in the nut forever: when one reaches the end of the loaded section it is scooped out by a return tube or deflector and carried back to the start of the circuit, so the same handful of recirculating balls cycles endlessly and the nut can travel the full length of any shaft.

Because of that efficiency, accuracy, and longevity, the ball screw is the default linear actuator wherever a controlled axis has to move a real load to a precise position thousands of times a day: the X, Y, and Z axes of CNC machine tools, the wafer stages of semiconductor lithography, the rams of all-electric injection-moulding machines, the electromechanical actuators that move aircraft flight surfaces, and the column of nearly every precision linear stage in a lab.

The mechanism — geometry of the rolling contact

The heart of a ball screw is the cross-section of the groove. A ball sitting in a single circular groove touches it at only one point, and a point contact under load develops enormous stress. So the groove is cut as a Gothic arch (two circular arcs forming a slightly pointed profile) or as a circular arc whose radius is a few percent larger than the ball. This gives two contact points per ball per side, spreads the Hertzian contact stress, and sets the contact angle — typically 45° — at which load is shared between the axial and radial directions.

The number of balls actually carrying load matters. They are distributed over several turns (typically 2.5 to 5 effective working turns inside the nut) and several circuits — each circuit being one closed loop of balls that recirculates through its own return path. More turns and more circuits share the thrust across more contacts, lowering the stress on each and raising both load rating and stiffness. The trade is that balls in different circuits must not collide at the pickup, and a longer ball path adds drag.

Recirculation comes in three common flavours, and the choice quietly sets the speed and noise of the whole machine:

• External return tube. A tube bolted to the outside of the nut scoops balls out of one or more turns and pipes them back. Simple, cheap, handles many turns per circuit, but the tube sticks out and the pickup is the speed-limiting element.
• Internal deflector (button). A small insert lifts the ball over a single thread crest and drops it into the adjacent groove, so each circuit is just one turn. Compact and quiet, low ball count per circuit, common on smaller precision screws.
• End-cap return. Balls are channelled axially through bores in the nut body from one end to the other. Used on high-lead and high-speed screws because the ball pickup is smooth and the geometry tolerates fast travel.

The governing equations — lead, thrust, and torque

The kinematics are simple and exact. The nut's linear speed v follows directly from the screw speed n and the lead L:

v = n · L          (linear speed = rev/min × lead)

Example:  n = 3000 rpm,  L = 10 mm
          v = 30,000 mm/min = 0.5 m/s = 30 m/min

The link between motor torque and the thrust force the nut delivers is where the ball screw earns its keep. The ideal (frictionless) relationship is set purely by lead; real performance is scaled by the efficiency η:

Driving rotation → linear:   T = (F · L) / (2π · η)

  F  = required axial thrust (N)
  L  = lead (m)
  η  = forward efficiency (0.90–0.95 typical)

Example:  push F = 5000 N,  L = 0.010 m,  η = 0.92
          T = (5000 × 0.010) / (2π × 0.92) = 8.65 N·m

Compare that to a plain lead screw of the same lead at η = 0.35: the torque demand becomes (5000 × 0.010) / (2π × 0.35) = 22.7 N·m — more than 2.5× the motor, the drive, and the heat. That single line is why electric injection-moulding and electric vehicle braking went to ball screws: the motor shrinks by a factor of two to three.

The reverse direction has its own efficiency η', and it explains a property that surprises people: a ball screw is almost always back-drivable. Push axially on the nut and the screw will spin. The back-driving efficiency is approximately:

η' = 2 − 1/η      (back-drive efficiency from forward efficiency)

  η = 0.92  →  η' = 0.91   (freely back-drives)
  A self-locking Acme screw has η < 0.5  →  η' < 0,
  i.e. it physically cannot be back-driven (it holds the load).

So the same low friction that makes the ball screw efficient also means it will not hold a suspended load by itself. A vertical ball-screw axis — a machine-tool spindle head, a press ram — needs a holding brake or a counterbalance, because if the servo loses power, gravity will spin the screw and the load will descend.

Worked example — sizing a CNC Z-axis

Suppose a vertical milling-machine Z-axis must lift a 200 kg head, accelerate it to 30 m/min in 0.1 s, and hold position to ±5 µm. Work the numbers in the order a designer actually does:

1. Lead and speed
   Target v = 30 m/min = 30,000 mm/min
   Servo max n = 3000 rpm  →  L = v/n = 10 mm lead

2. Thrust
   Static (gravity):  F_g = m·g = 200 × 9.81 = 1962 N
   Accel:  a = (0.5 m/s)/0.1 s = 5 m/s²  →  F_a = m·a = 1000 N
   Worst case lifting + accelerating:  F = 2962 N

3. Motor torque (η = 0.9)
   T = (F·L)/(2π·η) = (2962 × 0.010)/(2π × 0.9) = 5.24 N·m

4. Critical speed check
   Unsupported length 600 mm, fixed-supported ends, Ø25 mm root.
   n_crit ≈ 4.76e7 · d_r / L²  (mm, rpm, fixed-supported)
          ≈ 4.76e7 × 25 / 600² ≈ 3306 rpm
   Apply 0.8 safety →  2645 rpm usable < 3000 rpm needed:  TOO SLOW.
   Fix: support the lower end, or go to Ø32 mm root  →  n_crit ≈ 4230 rpm.  OK.

5. Hold the vertical load
   Back-drivable → fit a 24 V fail-safe spring brake on the motor.

The critical-speed step is the one beginners skip and then discover on the machine: a perfectly good thrust and torque calculation is useless if the slender screw whips into resonance before it reaches the target rpm. Lengthen the screw and the critical speed falls with the square of the length — double the span, quarter the safe speed.

Accuracy classes — rolled versus ground

Two manufacturing routes produce ball screws at wildly different price and precision. Rolled screws are cold-formed by pressing the blank between hardened dies; fast and cheap, with lead accuracy around 50 µm per 300 mm. Ground (and the newer precision-rolled) screws have the raceway finish-ground after hardening to a few microns per 300 mm. The ISO 3408 / JIS B 1192 accuracy grades quantify it:

Grade	Lead error (per 300 mm)	Method	Typical use
C0	±3.5 µm	Ground	Lithography stages, metrology, jig grinders
C3	±12 µm	Ground	CNC machining centres, precision robots
C5	±23 µm	Ground	General CNC, milling, lathes
C7	±52 µm	Rolled / ground	Transfer machines, general automation
C10	±210 µm	Rolled	Conveyors, clamps, low-cost actuators

Note that lead accuracy (does the nut end up where the maths says?) is separate from backlash (does it move at all when you first reverse?). A cheap C7 rolled screw can be fitted with a preloaded nut and have near-zero backlash while still drifting 50 µm over its length; a ground C3 screw nails both. For closed-loop CNC the linear encoder can correct lead error, so backlash and stiffness — both fixed by preload — often matter more than the raw grade.

Variants beyond the standard nut

• Single-nut, oversize-ball preload. One nut, with balls a couple of microns larger than nominal so they wedge in the Gothic-arch groove. Cheapest zero-backlash option; preload is fixed at build and cannot be re-adjusted.
• Double-nut, shim or spring preload. Two nut halves forced apart so each loads one groove flank. Preload is tunable and re-settable; spring preload self-compensates for wear. Standard on machine-tool axes.
• Rotating-nut (driven-nut) assembly. The nut is the driven element and the long screw stays still — or only the nut spins while the screw translates. Lets a very long axis run fast because the slender shaft never reaches its own critical speed. Used on long gantries and additive-manufacturing beds.
• High-lead / multi-start screws. Two to four parallel grooves multiply travel per turn. A 4-start, 10 mm-pitch screw gives 40 mm lead — 4 m/min at only 100 rpm — for high-speed pick-and-place where resolution is secondary.
• Ball spline. A close relative: balls run in straight axial grooves so the nut transmits torque while sliding freely along the shaft — the linear-bearing analogue of the ball screw, often paired with one on the same shaft.
• Planetary roller screw. Not a ball screw at all, but its direct rival at the high-load end: threaded rollers replace the balls, giving line contact, far higher load capacity and shock tolerance, finer lead, and much longer life — at higher cost. The choice for rocket thrust-vector actuators and heavy electric presses.

Where ball screws actually show up

• CNC machine tools. The original and still-largest market. Every milling machine, lathe, and machining-centre axis under about 2 m of travel uses a ground, double-nut, preloaded ball screw; the linear scale closes the loop and the screw provides the stiff, efficient drive. Above 2 m, linear motors increasingly take over because the screw's critical speed runs out.
• Semiconductor and electronics. Wafer-handling stages, die bonders, and PCB drilling machines use C0/C1 ground screws for sub-micron positioning, often in clean-room-compatible greaseless or sealed builds.
• All-electric injection moulding. Machines such as the Sumitomo and Toshiba all-electric lines use big ball screws for the clamp and injection rams, displacing hydraulics. The efficiency gain — no idling pump — cut energy use by 50 to 70 percent and is the main reason all-electric moulding took over precision parts.
• Aerospace electromechanical actuators (EMAs). The Boeing 787 and Airbus A380 use electric actuators built around ball or roller screws for spoilers, stabiliser trim, and thrust reversers as part of the move toward the more-electric aircraft, replacing centralised hydraulics. The 787's THSA (trimmable horizontal stabiliser actuator) is screw-driven.
• Automotive. Electric power steering, electronic parking brakes, active suspension, and electro-mechanical brake-by-wire callipers all use small ball screws to turn a compact motor's rotation into the linear force that used to come from hydraulics.
• Robotics and automation. Cartesian gantries, SCARA Z-axes, electric grippers, and 3D-printer beds use ball screws where the load and accuracy justify the cost over a belt or lead screw.
• Aerospace and ground-based positioning. Radio-telescope and solar-tracker drives, missile fin actuators, and aircraft seat and cargo systems all lean on ball or roller screws for their efficiency and back-up-power friendliness.

Failure modes — where ball screws actually break

• Contamination spalling. The number-one field failure. A single hard chip, casting grit, or grinding swarf dragged through the nut indents the raceway; the indent becomes a stress raiser that spalls and then unzips the whole track. Cure: wipers and seals on the nut, way-covers and bellows over the screw, and positive-pressure or labyrinth sealing in dirty environments.
• Lubricant starvation. Rolling contact needs an elastohydrodynamic oil film a fraction of a micron thick. Lose it and the balls and races metal-to-metal weld and tear (adhesive wear). Cure: automatic central lubrication, the right NLGI-2 grease or circulating oil, and respecting the relubrication interval (often every few hundred km of travel).
• Brinelling at the return. Over-speed or shock makes balls slam into the return-tube pickup, denting the groove. The machine then ticks once per revolution as balls roll over the dents. Cure: stay under the DN limit, avoid hard end-stops, and pick a high-speed return design for fast axes.
• Preload loss from wear. Every preloaded screw wears slowly; as the balls and races erode, preload drops and backlash creeps back, degrading positioning. Spring-preloaded double nuts self-compensate; shim-preloaded ones need periodic re-shimming. Monitoring reversal error over time predicts this.
• Whip and resonance. Running a long screw near its critical speed excites lateral vibration that wrecks the supports and the nut. Cure: support the screw mid-span, increase diameter, lower the max rpm, or switch to a rotating-nut or linear-motor drive.
• Buckling under compression. A long screw pushed in compression (rather than pulled in tension) can buckle as a column. End fixity and the column slenderness ratio set the limit; designers orient the load to put the screw in tension where possible.

How a ball screw compares to the alternatives

Property	Ball screw	Lead screw (Acme)	Belt drive	Roller screw
Efficiency	90–95 %	20–50 %	~95 %	80–90 %
Backlash	~0 (preloaded)	Low (anti-backlash nut)	Belt stretch / 20–50 µm	~0 (preloaded)
Positioning accuracy	Few µm	Tens of µm	50–200 µm	Sub-µm to few µm
Load capacity	High	Medium	Low–medium	Very high
Speed / lead range	High (DN-limited)	Low–medium	Very high	Medium
Self-locking	No (back-drives)	Often yes	No	No
Shock / debris tolerance	Low	Medium	Medium	High
Relative cost	Medium–high	Low	Low	Very high
Typical use	CNC axes, EMAs, presses	Clamps, jacks, manual feeds	Long fast gantries	Rocket actuators, heavy presses

Common pitfalls when applying ball screws

• Sizing on thrust alone and forgetting critical speed. The most common mistake: the torque maths checks out but the screw whips before it reaches the target rpm. Always run the critical-speed and DN checks before fixing the lead and diameter.
• Using a back-drivable screw to hold a vertical load. A ball screw is not self-locking. A vertical axis without a fail-safe brake will drop its load the instant power is lost. Fit a brake or counterbalance.
• Over-preloading for stiffness. Doubling preload to chase axial stiffness multiplies drag torque and heat and can halve life. Keep preload near 5–10 % of the dynamic load rating.
• Ignoring contamination. Ball screws are intolerant of dirt in a way lead screws are not. No way-cover, no scraper, no seal — no rated life. Budget the sealing and lubrication, not just the screw.
• Mismatching accuracy grade to the control loop. Paying for a C0 ground screw on an axis that already has a linear encoder wastes money — the encoder corrects lead error. Conversely, an open-loop axis lives or dies on the screw's raw grade.
• Putting the screw in compression. A long screw loaded in compression can buckle as a column; arrange the geometry to load it in tension, or shorten the unsupported length.