A ball screw with a 20 mm diameter and 40 mm lead has a 0.5:1 diameter-to-lead ratio, while a 30 mm diameter and 60 mm lead has a 0.5:1 ratio, showing that equal lead scaling does not increase the ratio.
For rigidity-focused motion systems, screw diameter, minor diameter, mounting arrangement and load path matter more than lead alone. Lead remains a speed and resolution decision, while diameter controls the elastic deflection of the screw, nut and support system.
What the diameter-to-lead ratio actually measures
The diameter-to-lead ratio is a useful screening number, not a rigidity rating. A 20 mm diameter with 20 mm lead gives 1.0:1, a 20 mm diameter with 40 mm lead gives 0.5:1, and a 30 mm diameter with 60 mm lead again gives 0.5:1.
Ball screw rigidity is normally treated as an assembly property, not a shaft-only property. The calculation uses elastic deformation in micrometres, axial force in newtons and total system rigidity in newtons per micrometre. The screw shaft, ball nut, support bearings, and nut and bearing housings all contribute to the result [S1].
The shaft contribution depends on the screw's minor diameter, the distance from the thrust bearing to the nut, and the end-bearing arrangement.
How lead changes speed, resolution and stiffness
Lead is the axial travel produced by one screw revolution, so linear speed equals lead multiplied by rotational speed. A 5 mm/rev screw running at 600 rpm produces a nominal 3,000 mm/min, or 50 mm/s [S5]. This makes lead a primary driver of feed rate, motor speed and positioning resolution.
For a motor rated at 3,000 min⁻¹ and a maximum carriage speed of 1 m/s, a lead of at least 20 mm is required. The calculation gives 1 × 1,000 × 60 ÷ 3,000 = 20 mm/rev.
Increasing lead can increase the helix angle and reduce the axial component of applied torque relative to torque input. Ball screws commonly achieve mechanical efficiency above 90% with rolling steel-ball contact, while a sliding lead screw transfers roughly 40% of input power to the workpiece [S3][S4]. Higher lead is useful for speed, but it is not a substitute for shaft stiffness.
Rigidity depends on diameter and support arrangement
For a fixed-free or fixed-floating screw arrangement, shaft rigidity is calculated from the screw's minor diameter, cross-sectional area, steel modulus and the distance between the thrust bearing and ball nut. With two fixed ends, the calculation uses the distances from the nut to each fixed bearing [S1].
This is why an end-support decision can outweigh a small increase in nominal screw diameter.
A larger diameter generally improves rigidity because it increases the shaft's cross-sectional area and usually allows a stiffer nut and end bearings.
Comparison of diameter-to-lead choices
Comparison of common sizing logic shows why diameter and lead must be separated.
For comparison across axes, a 30 mm diameter with 60 mm lead also gives 0.5:1, so it preserves the ratio but increases shaft size and does not change the lead-based speed relationship. These are screening conclusions, not substitutes for the rigidity, buckling and critical-speed checks.
Where each ratio fits in machine design
A high-lead, lower-diameter configuration suits high-speed transfer equipment where motor reduction, carriage speed and minimum feed per pulse dominate. The THK example uses a 60 kg table mass, a 20 kg work mass, a 1,000 mm stroke, a 1 m/s maximum speed, 0.15 mm backlash and ±0.3 mm positioning accuracy per 1,000 mm [S2].
A larger-diameter, lower-lead configuration suits applications where axial rigidity, repeated positioning accuracy, shock load or short settling time are more important than maximum feed per revolution. A 15 mm diameter with 20 mm lead appears in a selection example that separately calls for an accuracy grade matched to the application [S7]. For environmental or contamination-controlled applications, material and surface selection should be reviewed separately from the diameter-to-lead decision, as covered in 440C Ball Screws for Cleanroom and Vacuum Stages.
Ball screws are not automatic choices for every axis. A conventional lead screw remains credible for slower or intermittent adjustment when its load, wear, accuracy and thermal limits meet the duty. Ball screws are stronger candidates for frequent, efficient positioning, but the matching nut, lubrication, contamination control and support design still determine actual performance [S5].
Selection method for a rigid axis
Start with the required linear speed and encoder resolution. Select the lead that meets the feed-per-pulse target, then calculate the required motor speed. For the 1 m/s example, this produces a 20 mm/rev minimum lead; adding margin or selecting a larger lead changes the motor-speed and torque requirements [S2].
Next, size the screw shaft for the axial load, supported length, impact factor, buckling and critical speed. Use the minor diameter and bearing span in the rigidity calculation, not only the nominal diameter. Add the nut, support-bearing and housing stiffness values where available, and check the complete assembly against the allowable axial deflection.
Finally, specify the accuracy and axial-clearance requirements. The 1,000 mm stroke example requires lead-angle accuracy of ±0.09 mm/300 mm or higher and lists 0.15 mm backlash [S2]. Use the resulting diameter-to-lead ratio as a design record and comparison metric, not as a substitute for the full mechanical calculation.
The next trackable design check is the shaft diameter and lead pair against minimum feed per pulse, supported-length rigidity and critical speed. A practical specification should record lead, nominal and minor diameter, support method, axial load, accuracy grade and allowable axial deflection in one table.