Servo Motor Selection for Timing Belt vs. Ball Screw Linear Modules: A Torque, RPM, and Inertia Matching Guide

What will you do when you face a Servo Motor Selection for Timing Belt vs. Ball Screw Linear Modules?

Note to you: this article assumes you have already chosen between a timing belt linear module and a ball screw linear module — that decision (stroke, accuracy class, environment) is already covered on those product pages and on the linear modules overview. This article picks up one step later: once the drive type is fixed, how does the servo motor pairing need to change? 

Introduction

A servo motor sized correctly for a ball screw axis is not automatically correct for a timing belt axis carrying the same load — and the reverse is just as true. The two transmissions differ enough in stiffness, friction behavior, and rotating mass that reusing one torque/RPM/inertia sizing sheet across both routinely shows up as one of three symptoms: overload alarms during acceleration, audible resonance at high speed, or slow positioning drift over a production shift.

This guide walks through the three parameters that actually change between the two drive types — torque, rated RPM, and inertia ratio — with the underlying formulas shown rather than just referenced, one worked example labeled clearly as illustrative (not a customer case study), and links to where the real, model-specific numbers live: the module and servo datasheets.

What this article is not: a replacement for the servo drive manufacturer’s own sizing software or the ball screw catalog’s engineering tables. Treat the ranges below as a first-pass rationality check, then confirm against the specific hardware’s published data before finalizing a design.

1. Why the Same Servo Sizing Rules Don’t Transfer Between Belt and Screw Axes

The mechanical difference that matters for servo selection isn’t stroke or accuracy class (that’s a module-selection question, covered on the belt drive linear module page) — it’s transmission stiffness and rotating mass:

• A ball screw linear module is a rigid, low-backlash drivetrain. The screw shaft itself is a meaningful rotating mass, and the coupling between motor and load is stiff — good for positioning accuracy, but it means torque spikes and inertia mismatches transmit almost unfiltered back to the motor.
• A timing belt drivetrain has some built-in compliance (belt stretch) and a much lighter rotating assembly (pulleys, not a steel shaft). That compliance can act as a mechanical low-pass filter, but it also means the belt itself absorbs some of the motor’s torque output rather than transmitting all of it to the load.

Everything in Sections 2–4 follows from those two facts.

2. Torque Matching in Servo Motor Selection for Linear Modules

2.1 The formulas

Ball screw axis — torque at the motor shaft:

T_bs = (F × Ph) / (2π × η_bs)

Timing belt axis — torque at the motor shaft:

T_belt = (F × r_p) / η_belt

2.2 Safety margin — treat as a starting point, not a spec

Most servo sizing guides recommend building in a continuous-torque margin and a larger peak-torque margin for acceleration/shock events. Because ball screw axes reflect more of that shock load back to the motor (see Section 1), they typically warrant a larger peak margin than an equivalent belt axis. The exact multiplier depends on the servo drive’s own overload curve — check the drive manufacturer’s torque-speed chart rather than applying a fixed number across every project.

2.3 Illustrative worked example (not a customer case — round numbers for clarity)

Two axes, same 12 kg carriage, same 0.8 m/s² acceleration, same horizontal orientation:

The point of this table isn’t a specific N·m number — it’s that the direction of the difference (screw needs more torque margin than belt, for the same load and acceleration) is mechanically explainable, not an arbitrary rule. Run your own numbers through both formulas with your actual carriage mass, stroke, and the module’s published lead/pulley dimensions.

3. RPM and Linear Speed Matching in Servo Motor Selection for Linear Modules

3.1 Converting RPM to linear speed

• Ball screw: linear speed (mm/s) = servo RPM × lead (mm) / 60
• Timing belt: linear speed (mm/s) = servo RPM × pulley circumference (mm) × gear ratio / 60

3.2 The constraint that only applies to ball screws: critical speed

Every ball screw has a critical speed — the RPM above which the shaft begins to whip and resonate — determined by the screw’s root diameter, unsupported length, and end-fixity condition (fixed-fixed, fixed-supported, or supported-supported mounting). The standard engineering formula used across the ball screw industry is:

N_cr = (K × dr × 10^7) / L²

Timing belt drives have no equivalent critical-speed ceiling — pulley/belt systems don’t develop the same shaft-whip failure mode, which is one reason long, high-cycle-rate axes over roughly 2–3 meters more often default to belt drive. That module-level tradeoff (stroke vs. accuracy vs. drive type) is covered in more depth on the belt-driven linear modules page — this article is focused specifically on what it means for the servo’s RPM ceiling, not on re-litigating which drive type to pick.

4. Inertia Ratio Matching — and a Common Misconception to Correct

4.1 What the inertia ratio actually governs

The inertia ratio (reflected load inertia at the motor shaft ÷ motor rotor inertia) affects how easy the servo loop is to tune and how prone the system is to resonance and overshoot. The commonly cited industry rule of thumb, independent of drive type, is:

• 1:1 to 3:1 — ideal for high-performance, fast-settling axes
• up to roughly 10:1 — generally acceptable for standard industrial applications
• above that — tuning gets progressively harder and may require a larger motor, a gear reducer, or a mechanical redesign to bring reflected inertia down

(This range reflects widely published servo sizing guidance — see Power Electronics Group’s inertia matching primer for the underlying resonance/anti-resonance derivation.)

4.2 Where a fixed “belt gets a looser limit, screw gets a stricter one” rule breaks down

It’s tempting to assume timing belt axes tolerate a higher inertia ratio than ball screw axes because belt compliance “damps” the system. In practice, the more accurate variable is coupling/drivetrain stiffness, not “belt vs. screw” as a label — a stiff coupling (common on many ball screw axes) can actually tolerate a higher inertia mismatch than a compliant one, while a belt’s compliance can make some systems more sensitive to inertia mismatch, not less, depending on tensioning and belt length. In other words, the real governing factor is the stiffness of whatever sits between the motor rotor and the load, and that has to be evaluated per-axis rather than assumed from the drive-type label alone.

Practical takeaway: use the 1:1–10:1 range as your starting filter regardless of drive type, then confirm with the servo drive’s auto-tuning or inertia-estimation function on the actual assembled axis — that reading is more reliable than any generic split-by-drive-type rule.

5. Matching to an Actual Servo Line

To make this concrete rather than abstract: TallMan’s linear modules pair with the Delta ECM-B3 standard servo system, offered across a 100W–3kW power range and in high-, medium-, and low-inertia rotor variants —

• Low-inertia motors suit fast start-stop cycles and high-response positioning — a natural fit for lightweight timing belt axes with frequent reversals.
• Medium-inertia motors cover general-purpose axes of either drive type.
• High-inertia motors suit applications needing speed stability or resistance to external disturbance forces — relevant for longer ball screw axes carrying a heavier reflected load.

That inertia-class selection is a more direct lever than trying to force every axis toward one universal ratio target.

6. Vertical (Z-Axis) and Duty-Cycle Adjustments

Two conditions push the sizing above the horizontal-axis baseline calculated in Section 2, on either drive type:

• Vertical orientation: gravity acts on the axis continuously, not just during acceleration. Both drive types need a holding brake for power-loss conditions, and the continuous torque requirement should be recalculated with the static gravity load included, not just added as a flat percentage on top of the horizontal number. TallMan’s heavy-duty linear module series is worth reviewing for higher-load vertical or cantilevered layouts.
• High-duty-cycle / continuous operation: 24/7 lines running at or near 100% duty cycle generate sustained motor heat. Confirm the continuous torque figure against the servo’s thermal (RMS) rating for the actual duty cycle, not just the peak torque capability.

7. Quick Reference Checklist in Servo Motor Selection for Linear Modules

Frequently Asked Questions

Can I use the same servo motor model on a belt axis and a screw axis carrying the same load?

Not as a default assumption. The torque formulas alone (Section 2.1) produce different numbers for the same mass and acceleration because of the lead-vs-pulley-radius difference, before safety margins are even applied. Run both calculations rather than assuming they land the same.

Does a longer ball screw always need a lower-RPM servo?

Only if the resulting RPM would exceed that specific screw’s calculated critical speed (Section 3.2), which depends on unsupported length, root diameter, and end-fixity — not on stroke length alone. Check the screw’s engineering table rather than applying a flat RPM cap.

Is a high-inertia servo required for every ball screw axis?

No — it depends on the reflected load inertia at the motor shaft for that specific axis, not on drive type by default. A short, lightly loaded screw axis may be fine with a medium-inertia motor; a long axis with a heavy carriage may need the high-inertia variant discussed in Section 5.

What actually fixes positioning drift on a belt gantry?

Belt stretch under repeated load cycling is the usual mechanical cause. The servo-side lever is increasing continuous torque reserve to counteract that stretch; on the mechanical side, belt tension and pulley wear should also be checked, since a servo change can’t fully compensate for a mechanical belt problem.

Where to Go From Here

If the drive type is already decided and the open question is which specific servo motor and drive pair with a particular belt or screw module for a given load, stroke, and cycle rate, TallMan’s engineering team can review the specific axis parameters against the Delta ECM-B3 servo range and the module’s published datasheet. Full model specifications and e-catalogues are available on the download center.