KEVOS® MAKEOS · Mechanics
Ball-Screw Linear Axis Sizing
Can this ball screw and motor move the load at the speed and acceleration required, and how long will the screw last?
Sizing of a ball-screw driven axis over a move cycle: screw speed, axial forces while accelerating, running and decelerating, motor torque in each phase from the handbook driving-torque relation plus rotor and screw inertia, RMS torque over the cycle, critical speed and buckling load for the end fixity, cubic-mean load and rating life in hours.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load and motion | ||
| Moving mass | kg | Mass of the carriage and load. |
| Guide friction coefficient | Friction coefficient of the linear guides. | |
| External axial force while moving | N | Process or external force opposing motion. |
| Maximum speed | mm/s | Top linear speed. |
| Acceleration (and deceleration) time | s | Time to reach top speed (the same for stopping). |
| Constant-speed time | s | Time at constant speed in each move. |
| Dwell time per cycle | s | Stationary time per cycle. |
| Screw and drive | ||
| Lead | mm | Screw lead (travel per revolution). |
| Root diameter | mm | Root diameter of the screw. |
| Length between supports | mm | Unsupported length between bearings. |
| End fixity | choice | Mounting of the screw ends. |
| Screw efficiency | % | Ball-screw efficiency (about 90%). |
| Motor and coupling inertia | kg·m² | Rotor plus coupling inertia. |
| Dynamic load rating | kN | Dynamic load rating of the ball nut. |
| Load factor | Load factor for vibration and shock. | |
| Required life | h | Life you need in hours of this cycle. |
| Limits | ||
| Allowed share of critical speed | % | Share of critical speed allowed. |
| Allowed share of buckling load | % | Share of buckling load allowed. |
| Screw modulus | GPa | Elastic modulus of the screw. |
| Screw density | kg/m³ | Density of the screw. |
Method and formulas
- Screw speed n = v ÷ lead; acceleration a = v ÷ t_a; axial force = external + μ m g ± m a.
- Drive torque T = F × lead ÷ (2π e) (handbook ball-screw driving torque) plus (J_motor + J_screw) α when accelerating.
- RMS torque = √[Σ T² t ÷ cycle time]; critical speed and buckling as the screw-limits tool (same end-fixity factors).
- Cubic-mean load weighted by travel; life = (C_a ÷ f_w F_m)³ × 10⁶ revolutions.
- Example: 200 kg at 500 mm/s on a 10 mm lead needs 2.3109 N·m peak and 1.0149 N·m RMS.
Limitations
- Horizontal axis; vertical axes add the load weight to every phase.
- Screw inertia uses the root diameter (slightly low).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a ball screw and servo motor for a linear axis
- Check an existing axis for a faster cycle
- Find whether speed, buckling, torque or life limits the axis
Who it is for
- Machine designers
- Automation engineers
- Design engineers
What you get
- Screw speed, forces and motor torques
- Critical speed and buckling checks
- Cubic-mean load and life
Interpreting the result
- If critical speed limits, use a coarser lead, a stiffer end support, or a rotating nut.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2561–2563. Topic reference; no source tables or recommended settings are reproduced.
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