Experimental Study on the Effect of Ball Screw Circulation Methods on Transmission Efficiency

Ball screw transmission efficiency is a critical performance metric in precision motion systems, and the ball circulation method—external, internal, or end-cap—plays a decisive role in determining friction losses, torque characteristics, and high-speed capability. This experimental study compares the measured efficiency of lead screws employing different circulation structures under controlled load and speed conditions. The results provide engineers with practical selection guidance for optimizing drive performance in machine tools, semiconductor equipment, and high-speed automation.

Technical Overview

A ball screw is a mechanical linear actuator that translates rotational motion into linear motion with minimal friction, achieved by recirculating hardened steel balls between the screw shaft and the nut. While theoretical efficiency of a ball screw typically ranges between 90% and 95%, the actual measured efficiency depends heavily on the design of the ball circulation path. Each time a ball completes one circuit along the thread groove, it must be guided back to the start of the circuit through a return channel, and the geometry of this return path directly influences ball collision, friction, vibration, and torque ripple.

Three principal circulation methods dominate modern ball screw design: external circulation using a return tube, internal circulation using an embedded reverser, and end-cap circulation that returns balls through holes machined in the nut body. The experiment described in this article was designed to quantify how each circulation method affects transmission efficiency under identical shaft diameter, lead, preload class, and lubrication conditions, so that the measured differences can be attributed to the circulation structure itself rather than to unrelated manufacturing variables.

Testing Samples

Three groups of test screws were prepared with matched nominal specifications—a nominal diameter of 40 mm, a lead of 10 mm, a C3 accuracy grade, and a medium double-nut preload—but with different circulation architectures. All samples were manufactured from the same material batch and ground on the same production line to eliminate batch-to-batch deviation.

External Circulation Type (Tube Return)

In this construction, balls exit the loaded thread groove at the end of a circuit and are lifted out of the nut by a pickup finger, then guided through a return tube mounted on the outside of the nut before re-entering the groove. This design allows multiple independent circuits, a large ball count, and high load capacity. However, the external tube increases the overall nut envelope, and the ball pickup zone introduces a brief acceleration event that can generate torque ripple at elevated speeds.

Internal Circulation Type (Reverser Return)

This type returns balls through a reverser insert seated in the nut wall. Each circuit spans approximately one thread turn, and the ball is forced across the thread crest back to the adjacent groove. The construction is compact, with a small nut outer diameter and low inertia, making it suitable for space-constrained assemblies. The trade-off is a sharp reversal at the reverser ramp, where adjacent balls from neighboring circuits may contact each other and produce friction losses and noise, particularly at higher rotational speeds.

End-Cap Circulation Type

In the end-cap design, balls travel axially through return holes drilled longitudinally in the nut body and are redirected at each end by cap plates. Because the balls maintain an axial orientation through the return path, they avoid the violent reversals of the internal type, which permits significantly higher critical speed values and higher dN ratings. The nut diameter remains moderate, and the circuit arrangement is highly flexible, though the end-cap structure adds components and assembly complexity.

Testing Items

The experiment evaluated the following performance parameters for each circulation method under a common test matrix:

• Transmission efficiency at rated axial load across a range of rotational speeds
• Input torque versus generated axial thrust (torque-thrust coefficient)
• Friction torque and torque ripple under no-load and preload conditions
• Efficiency variation under different axial loads (25%, 50%, and 100% of dynamic load rating fraction)
• Friction torque stability and efficiency drift during continuous operation
• Nut surface temperature rise as an indirect indicator of frictional power loss
• Vibration and acoustic noise signatures at high rotational speed
• Forward-drive efficiency versus back-drive efficiency

Testing Methods

All tests were performed on a servo-driven ball screw performance test bench in a climate-controlled laboratory maintained at 20 ± 1 °C. The test bench consists of a servo motor with an integrated high-precision torque transducer on the input side, precision support bearings with a fixed-fixed mounting arrangement, and a magnetically controlled electromagnetic loading actuator that applies a calibrated axial force to the moving table. Linear position and velocity were captured by a linear encoder with 0.1 µm resolution, and all channels were sampled synchronously at 10 kHz through a dedicated data acquisition system.

Transmission efficiency was calculated from the measured input torque and the corresponding axial thrust using the fundamental relationship: efficiency equals the useful output work divided by the input work, expressed as the axial force multiplied by the lead divided by two pi multiplied by the measured driving torque. Back-drive efficiency was measured inversely by applying an axial force and recording the resulting output torque. Each test point was run for a stabilization period, followed by sixty seconds of continuous acquisition, with the reported value representing the mean of at least five repetitions to ensure statistical validity.

The speed sweep covered 500, 1000, 1500, 2000, and 3000 rpm, and the internal circulation sample was additionally limited in its upper speed test in accordance with its lower dN rating. All samples were lubricated with the same lithium-based grease applied in equal quantity before each run, and a run-in procedure of 500 full strokes was completed prior to formal data collection to seat the balls and distribute the lubricant uniformly.

Test Results and Analysis

At moderate speeds below 1000 rpm, all three circulation methods demonstrated high efficiency, with measured values between 91% and 94%, confirming that the rolling contact mechanism itself dominates the loss profile under low-speed conditions. As rotational speed increased, the samples diverged noticeably. The end-cap circulation sample retained efficiency above 90% at 3000 rpm with the smallest torque ripple, while the internal circulation sample exhibited a measurable efficiency decline at speeds beyond 2000 rpm, accompanied by elevated noise attributable to ball-to-ball collision at the reverser ramps. The external tube type occupied an intermediate position, showing gradual efficiency reduction driven by turbulence and impact at the pickup zone while maintaining excellent performance under heavy load at moderate speed.

Under increasing axial load, all samples displayed a rising efficiency trend that gradually plateaued, consistent with the theoretical behavior of rolling friction, where the preload-induced friction torque becomes proportionally less significant as the working load grows. Temperature rise measurements correlated well with efficiency loss: the internal circulation sample recorded the highest nut temperature rise at high speed, confirming that a portion of the reverser-related losses was dissipating as heat. Back-drive efficiency followed the same relative ranking among the three types, typically measuring two to four percentage points below the corresponding forward-drive values.

Applications

The experimental findings support targeted selection of circulation methods according to the duty profile of the application:

• High-speed machine tool feed axes and high-speed gantry positioning favor end-cap circulation for its sustained efficiency and low torque ripple at elevated rpm
• Heavy-load transfer mechanisms, presses, and injection molding machine clamping units benefit from external tube circulation with multiple circuits and high load capacity
• Compact actuators, medical devices, and instrumentation with space and inertia constraints are well served by internal reverser circulation at moderate speeds
• Semiconductor wafer handlers and inspection stages requiring smooth, quiet, low-heat operation should prioritize end-cap or external circulation depending on stroke and speed envelope
• Vertical axes with back-drive concerns should account for the measured back-drive efficiency differences when sizing brakes and counterbalance systems

FAQ

Which circulation method achieved the highest efficiency in the experiment?

The end-cap circulation type achieved the highest and most stable efficiency across the full speed range, sustaining values above 90% even at 3000 rpm. The external tube type was comparable under heavy load and moderate speed, while the internal reverser type was most efficient at low to moderate speeds and in compact assemblies.

Why does internal circulation lose efficiency at high speed?

At high rotational speed, balls arriving at the reverser must undergo a rapid direction change within a very short arc, causing impacts between adjacent balls from consecutive circuits. These collisions convert kinetic energy into frictional heat and noise, increasing torque ripple and reducing net transmission efficiency. This is also why internal circulation screws carry lower recommended dN limits.

How was efficiency calculated in the test?

Efficiency was computed as the ratio of useful mechanical output to mechanical input: the axial force multiplied by the lead, divided by two pi multiplied by the measured input torque. High-precision torque and force transducers, combined with synchronous data acquisition, ensured that measurement uncertainty remained within one percentage point.

Do these results apply to rolled ball screws as well?

The relative ranking among circulation methods is expected to hold for rolled screws, but absolute efficiency values will be lower—typically by two to four percentage points—due to the rougher thread surface of rolled grooves. For critical efficiency-sensitive designs, ground screws with an optimized circulation structure are recommended.

How should preload be considered when interpreting efficiency data?

Preload adds a constant friction torque component that reduces efficiency at light loads. Because all samples in this experiment shared the same preload class, the reported differences reflect circulation geometry. In service, an oversized preload will depress measured efficiency for any circulation type, so preload should be matched to the actual load spectrum.