Backlash and Lost Motion
After a feed screw reverses, the handwheel turns through the thread clearance before the carriage moves. Predict that dead band from clearance and lead, and finish every approach in one direction.
The dial counts screw rotation; the indicator finds the carriage
The dial counts screw rotation; the indicator finds the carriage
A handwheel dial does not measure the carriage. It counts how far the screw has turned and multiplies by the lead. That is the carriage's travel only while the screw keeps pushing the nut in one direction.
A screw and its nut need some clearance between their thread flanks (a flank is the sloping side of a thread). After the screw changes direction, it must turn through that clearance before its other flank meets the nut and the carriage moves again. That clearance is backlash, the same idea defined for threads in Screw Threads and for gear teeth in Gear Drives and Tooth Geometry. The turn spent crossing it is lost motion: input that produces no output.
- Dial reading: travel predicted from screw rotation,
turns × lead. See Lead Screws. - Carriage position: where the carriage really is, as an indicator touching it would show.
- The difference is zero after a forward approach (the direction the dial was zeroed in) and one full clearance after a reverse approach.
Where the definition comes from
Modern Machine Shop's column Eliminate Backlash From Machining Centers (Mike Lynch, 2000) defines backlash as “any non-movement that occurs during axis reversals.” This page uses the CourseWiki definition on Screw Threads: clearance that must be taken up after reversing before the load moves. In a real drive, elastic deflection can add lost motion as well; the lab below leaves it out.
Experiment: reverse the handwheel and watch the carriage wait; Interactive
Experiment: reverse the handwheel and watch the carriage wait
What the lab does: a handwheel turns an axially fixed lead screw. The dial reports travel calculated from screw rotation; an indicator on the carriage reports where the carriage really is. With a total axial clearance B between screw and nut flanks, the two agree only while the screw keeps pushing in the direction the dial was set in.
Dead band after a reversal = clearance ÷ lead, as a fraction of a turn:
angle = 360° × B ÷ L dial divisions = B ÷ (L ÷ 100) on a dial with 100 divisions per turn.
Worked example: lead L = 5 mm/rev, so one division is 0.05 mm. Clearance B = 0.20 mm. Angle = 360° × 0.20 ÷ 5 = 14.4°; divisions = 0.20 ÷ 0.05 = 4. For four divisions after the reversal the dial changes and the carriage does not.
Landing on 25.00 mm after overshooting to 25.60 mm (lead 5 mm, clearance 0.20 mm). The dial was zeroed after a forward approach, so it equals the carriage position only for forward approaches:
| Method | Dial moves | Dial | Carriage | Error |
|---|---|---|---|---|
| Reverse straight to the number | 25.60 → 25.00 mm | 25.00 mm | 25.20 mm | +0.20 mm |
| Back past it, approach forward again | 25.60 → 24.50 → 25.00 mm | 25.00 mm | 25.00 mm | 0.00 mm |
Reversing straight to the number stops the carriage one full clearance away from the dial reading, still on the overshoot side: the dial shows 25.00 mm while the carriage is at 25.20 mm. Backing past the target by more than the clearance and finishing in the original direction puts the screw back on the flank the dial was set against.
Model limits: rigid parts and a kinematic dead band only. Friction is assumed to hold the carriage still inside the clearance, and nothing else pushes it along the axis; there is no force, stiffness, preload or stick-slip model. Lead, clearance and the 3D dimensions are illustrative and exaggerated, not a standard thread or a measured machine.
Predict the dead band: clearance divided by lead, as a fraction of a turn
Predict the dead band: clearance divided by lead, as a fraction of a turn
Once the screw reverses, the carriage stays still until the screw's helix has moved one full clearance B. One turn moves the helix one lead L, so the dead band is B ÷ L of a turn.
dead-band angle = 360° × B ÷ L
dead-band divisions = B ÷ (value of one division); with 100 divisions per turn, one division is L ÷ 100.
| Lead L | One division | Clearance B | Dead band |
|---|---|---|---|
| 5 mm/rev | 0.05 mm | 0.20 mm | 4 divisions = 14.4° |
| 2 mm/rev | 0.02 mm | 0.20 mm | 10 divisions = 36° |
The carriage error after a reverse approach is the same 0.20 mm in both rows. A finer lead only spreads that same clearance over more of the handwheel turn.
Land on a dimension: finish every approach in the direction the dial was set
Land on a dimension: finish every approach in the direction the dial was set
If you overshoot a target, turning straight back to the number leaves the carriage one clearance away from it, because the screw is now pushing on the other flank. Instead:
- Back the handwheel past the target by more than the backlash.
- Turn in the original direction again and stop on the number.
The same reasoning applies when setting a dial. MIT's 2.670 milling notes say to “be certain that the backlash in the mechanism driving the table is taken up prior to setting the dial indicator”. A dial set with the clearance taken up in one direction reads true for approaches in that direction. For edge finding, Mill Indicators and Part Zero repeats the touch from the same direction for the same reason.
A readout that measures the slide, and when the clearance still matters
The MIT 2.670 milling machine notes (section “Using the Micrometer Dials”) also point out that a digital readout measures the bed position directly, so its reading is not thrown off by backlash. The clearance is still in the drive. A force that pushes the carriage along the screw can move it across the clearance without the handwheel turning; Climb and Conventional Milling explains when a cutting force does that.
What the lab model includes and leaves out
What the lab model includes and leaves out
- Included: a rigid screw that turns but never slides along its axis, a nut fixed to the carriage, and a total axial clearance B. The carriage position c stays within B/2 of the screw's helical phase s = −Lφ/360° (right-hand thread, φ the screw rotation); inside that band it does not move.
- Assumed: friction holds the carriage still inside the clearance, and no outside force pushes it along the axis.
- Left out: forces, friction values, stiffness and elastic wind-up, preload, stick-slip and wear. Drives designed to remove the clearance, such as preloaded ball nuts or adjustable split nuts, are beyond this model.
- Illustrative: the leads, clearances and the 3D screw (5 mm lead, 1.0 mm clearance, 30° flanks) are chosen to be seen, not taken from a standard thread or a measured machine.
For drive design in depth, Alexander Slocum's Precision Machine Design (1992) covers actuators and transmissions in Chapter 10, including section 10.8, Linear Power Transmission Elements.
Mill around an island: X and Y backlash change the material left behind; Interactive
Mill around an island: X and Y backlash change the material left behind
A perfect 4 mm diameter cutter makes one contour groove around a 24 mm circular island. The dashed outline is the intended island; span errors compare with zero backlash. Material in the middle and outside the groove remains: this is not a pocket-clearing path. Only X/Y drive clearance changes.
All four start at the right side and run counterclockwise. Before the plunge, both axes approach the start in their positive directions and the coordinates are calibrated there. On reversal, the actual cutter can stay still along one axis while moving along the other. Its full circular footprint removes material along that path.
The spans above are sections through X = 0 or Y = 0, not a best-fit circle or the greatest overall width. They come from intersections with the swept cutter, not pixel counting. Changing the start, winding or initial seating can change the local shape; do not infer that every circle becomes the same oval.
Approximation: circular paths use 1° chords (under 0.001 mm sag here). These printed diagrams use 0.20 mm cells; the live area shading uses 0.10 mm cells. The millimetre span readings use the underlying swept chords.
The cutter removes the upper layer at one fixed depth. Grey is material still at its original height; the groove floor is not drawn. A boundary pass leaves both an island and the surrounding stock, so it is not a cleared pocket. The dashed line is the intended island boundary, not the cutter-centre path: that path is one cutter radius outside it.
What the model means, and why it is not a prediction for every CNC
The coordinates describe the cutter relative to the workpiece, viewed from above: +X right, +Y up. A moving table travels in the opposite sense. The drive infers position from motor/screw motion, with no compensation or linear-position correction. The first approach seats both axes and calibrates the coordinates at the start, before the plunge. That reference is kept through the cut.
With positive initial seating, each actual coordinate c is updated as c = min(max(c, q), q + B), where q is the motor-inferred coordinate and B the total clearance. Negative seating uses the band [q − B, q]. These are shifted forms of the same play operator as the screw lab above. Each axis holds until a band edge reaches it. If the axes take up clearance at different moments within a command segment, the actual path has an extra bend; the cutter sweep includes it.
Every cut segment removes a disc swept along that actual segment, a capsule with the cutter's 2 mm radius. The area shading compares the actual and zero-backlash histories at the same command step. Span measurements intersect those capsules with the two centre sections. They are not a best-fit diameter, an overall size tolerance or a guarantee of the rest of the contour.
All other effects are idealized away: no runout, deflection, wear, servo lag, cutting-force pull, thermal error or compensation. Friction is assumed to hold a slide inside its clearance. The shapes, clearance settings and viewing speed are illustrative. Restart begins a fresh workpiece; changing a setting recomputes the experiment.
HEIDENHAIN describes direct linear-axis measurement as working “without intervening mechanical elements”. Such feedback changes what the controller can observe; this lab deliberately does not model that correction. Haas's ballbar interpretation guide distinguishes lost motion at reversal from controller-related reversal spikes. Only rigid lost motion is included here.