Choose a ball screw lead so that one encoder count produces no more than 1 µm of commanded linear travel, then treat that value as a command-resolution limit rather than a guarantee of absolute accuracy.
The usable selection range depends on encoder resolution, screw lead, servo control, nut clearance, axis rigidity, and the difference between 1 µm resolution, repeatability, and absolute positioning accuracy.
Define the 1 Micron Requirement Before Selecting Lead
Resolution is the smallest positional increment that can be commanded, while accuracy is the difference between commanded and realized position and repeatability is the spread between repeated returns to the same point [S2]. These are separate specifications. A 1 µm command increment does not establish 1 µm accuracy or bidirectional repeatability.
The referenced design uses a 1 µm resolution-and-repeatability target across a 500 mm stroke [S3]. For a 500 mm axis, the referenced design targets resolution and repeatability of 1 µm [S3].
Do not use the 1 µm requirement to request a nut with 1 µm backlash. If the specification means 1 µm bidirectional repeatability, the mechanical reversal error must be below that value. If it means absolute accuracy over a specified stroke, screw lead error, mounting error, thermal expansion, and sensor calibration also enter the budget [S1][S3].
Calculate Lead from Encoder Counts
The fundamental relationship is linear travel per encoder count, or linear resolution, equals screw lead divided by usable encoder counts per motor revolution. A 10 mm lead with 2048 pulses per revolution produces 4.88 µm per pulse, equivalent to 0.00488 mm [S4]. A configuration based on that 10 mm screw therefore cannot deliver a 1 µm command increment through 2048-count feedback alone.
For a target resolution of 0.001 mm per count, required counts per revolution equal lead in millimetres divided by 0.001. The same equation becomes 1000 times the lead in millimetres for 1 µm resolution. A 2 mm lead requires 2000 counts per revolution, a 5 mm lead requires 5000, a 10 mm lead requires 10,000, and a 20 mm lead requires 20,000 [S2].
Do not assume that nominal encoder lines equal usable servo feedback counts. Dover's RE-2000 encoder has 500 lines, with counting electronics providing four counts per line and therefore 2000 counts per revolution [S2]. Electronic multiplication may increase the commanded count density, but it cannot create missing physical feedback information or remove mechanical error.
Compare Short, Medium, and Long Leads
Short leads favor command resolution and positioning sensitivity, but require more motor revolutions for a given travel and impose higher rotational-speed requirements. A 2 mm lead was identified for a 1 µm-resolution arrangement using a 200-step motor with divide-by-10 microstepping [S2]. That stepper arrangement does not transfer directly to a servo encoder, whose usable count density must be measured from the actual feedback specification.
Medium leads create a practical compromise for general servo axes. THK's example selection specifies a minimum feed amount of 0.02 mm/pulse [S1]. That example targeted 0.02 mm per pulse, not 1 µm, so its lead-and-count combinations must not be presented as 1 µm solutions.
Long leads maximize travel per revolution and reduce the number of motor revolutions required, but they magnify angular-error effects and make fine positioning more demanding. A 25 mm lead covers substantial distance per revolution and is associated with difficult sub-micron positioning [S7]. Long-lead axes suit rapid transfer, high-speed cycling, or long strokes where 1 µm command resolution is not required across the full operating envelope.
A useful comparison is lead versus required feedback density versus likely duty. A 2 mm lead needs at least 2000 counts for 1 µm resolution and suits precision, low-speed positioning; a 5 mm lead needs at least 5000 counts and reduces required speed; a 10 mm lead needs at least 10,000 counts and suits higher-throughput axes; a 20 mm lead needs at least 20,000 counts and is appropriate mainly where travel per revolution outweighs positioning sensitivity [S2][S7].
Apply Lead, Speed, and Thrust Constraints
Maximum motor speed constrains the lead because linear speed equals motor speed multiplied by lead. In THK's worked example, 3000 min⁻¹ and a target speed of 1 m/s produced a minimum calculated lead of 20 mm: 1,000 mm/s multiplied by 60 and divided by 3000 gives 20 mm per revolution [S1]. A 2 mm lead with the same 3000 min⁻¹ motor would support only 100 mm/s.
Thrust requirement must be checked separately. The axial force needed to accelerate and move the load depends on mass, acceleration, friction, and gravity for a vertical axis, while the motor must also overcome screw inertia and supply the thrust required by that load. The referenced 1 µm-axis design identifies thermal expansion, screw mapping residuals, encoder quantization, structural elasticity, and nut stick-slip friction as dominant error sources [S3].
Vertical axes require a brake or another assured holding method. Oriental Motor's selection example addresses an electromagnetic-brake motor for a vertically operated table driven through a ball screw, with motor selection tied to the operating duty [S8]. Do not use a high-lead screw to solve motor-speed limits without checking torque, axial-load capacity, critical speed, and brake requirements.
Specify Accuracy Grade and Backlash
ISO 3408 classifies ball screw accuracy from C0, the most precise, through C10, the least precise; C1, C3, and C7 are common selection levels for precision axes [S3]. The grade must be tied to a stated travel-distance error, not selected from the letter alone.
THK's worked example relates a required positioning accuracy of ±0.3 mm per 1000 mm to a lead-angle requirement of ±0.09 mm per 300 mm. It selects C7, whose cited travel-distance error is ±0.05 mm per 300 mm, and separately requires axial clearance of no more than 0.15 mm [S1]. That selection suits the stated ±0.1 mm repeatability and 0.02 mm-per-pulse feed requirement, not a 1 µm target.
For 1 µm repeatability, specify the nut's axial clearance, preload, and permissible variation as explicit procurement limits. A C-grade alone does not guarantee low backlash, and low backlash alone does not guarantee 1 µm accuracy. The ball screw and its nut must be specified as an accuracy-controlled assembly when positioning depends on reversal behavior.
Control the Full Precision Axis
The mechanical and feedback architecture can outweigh nominal encoder resolution. A 1 µm glass linear scale with a 0.1 to 0.5 µm accuracy class still requires calibration, mapping, and thermal compensation to reach the stated target [S3]. Linear-encoder or laser-interferometer resolution is independent of screw pitch because the feedback measures linear position directly [S2].
For a rotary-encoder ball-screw axis, the controller must close the loop on position rather than rely only on motor pulses. A speed-command arrangement can use encoder feedback and a PID position loop, but an analog speed interface does not itself provide servo positioning resolution [S4]. The controller's commanded-count interpretation, electronic subdivision, following error, and settling behavior must be matched to the mechanical system.
Use a rigid linear guide arrangement, minimize unsupported nut length, control nut rotation, and verify travel over the complete stroke. The referenced precision design suggests first structural modes above 200 Hz for a stiff gantry and above 400 Hz for production-class machines, while limiting guide cantilevers to less than four times the guide footprint [S3].
Identify Where a Rotary Encoder Is the Wrong Choice
Do not select a rotary encoder with a conventional ball screw when the requirement is unambiguous 1 µm absolute accuracy over a long stroke, especially where thermal expansion and lead error dominate. Linear feedback directly measures axis position and removes screw lead error from the feedback path, although mechanical compliance and feedback-device accuracy still remain [S2].
Do not select the shortest available lead merely to improve resolution. Very short leads increase motor speed demand and may reduce thrust capacity because motor torque is converted to force through a smaller lever arm. A 1 µm axis may require a higher-resolution encoder, a better nut and support system, lower structural deflection, and a tighter control loop, not only a 2 mm screw.
The standard linear-feedback alternatives are a linear encoder measuring position directly, a laser interferometer providing 10 nm single-pass or 5 nm double-pass resolution, or a linear motor whose position still requires a linear measurement device [S2]. These options make sense when screw mapping, backlash, and lead compensation are incompatible with the accuracy target.
Build the Final Selection Checklist
Start with the required stroke, maximum linear speed, acceleration time, payload mass, direction of travel, and whether 1 µm means command resolution, bidirectional repeatability, or absolute accuracy. The THK example combines a 1000 mm stroke, 1 m/s maximum speed, 0.15 s acceleration, 0.15 s deceleration, 60 kg table mass, 20 kg work mass, and eight reciprocations per minute [S1]. Those conditions determine the mechanical and motor checks that remain after lead selection.
Calculate required encoder counts from the selected lead, verify maximum motor speed, check axial load and ball screw life, select a suitable ISO 3408 accuracy grade, state the maximum axial clearance, and require measured repeatability and travel error over the specified stroke. Stop if a 1 µm command requirement cannot be met by the actual feedback count density or if the mechanical error budget exceeds the application target.
A sensible shortlist therefore contains a low-lead precision screw with a high-count rotary encoder for moderate-speed positioning, a direct linear-feedback stage when absolute accuracy dominates, and a long-lead high-speed screw for transfer duty where 1 µm resolution is not the governing requirement. Verify the selected assembly with the actual servo, encoder, controller, support arrangement, and operating load.