Motor Sizing Calculator (Torque & Inertia)
Load torque, inertia ratio, acceleration torque, RMS torque and required power for ball-screw, belt and rack drives and rotary tables, with a safety margin
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Estimates the torque, inertia ratio and power a motor needs to move a load on a ball screw, belt, rack or rotary table through a point-to-point cycle. A first pass at servo or stepper sizing.
How to use
- Choose the "Mechanism" and, for a linear axis, "Horizontal" or "Vertical".
- Enter the "Moving mass", "Friction coefficient of the guide" and any "External force against the motion".
- Enter the "Maximum speed", "Stroke per move", "Acceleration time", "Deceleration time" and "Dwell time after the move".
- Fill in the mechanism data, the reduction ratio, the "Motor rotor inertia" from the catalogue and a "Safety factor".
- Read the peak torque, RMS torque, inertia ratio and motor speed at the top, and the recommended values below the chart.
How it works
- Load torque: ball screw T = F × lead ÷ (2π × η); belt or rack T = F × D ÷ (2 × η). F = external force + m × g (vertical) or μ × m × g (horizontal).
- Acceleration torque = (load + rotor inertia) × α, α = 2π × N ÷ 60 ÷ acceleration time. A reducer of ratio i divides torque by i and inertia by i².
- RMS torque = √(Σ T² × t ÷ Σ t) over the four phases. Power = torque × 2π × N ÷ 60.
- All values are estimates; stiffness, resonance, heating and regeneration are not covered. Confirm the motor with the maker's selection software.
Questions and answers
- What inertia ratio is acceptable for a servo motor?
- Many makers recommend 5 or less for fast positioning; 5 to 10 often works with tuning. The bands shown are guidelines, not a standard.
- How do I calculate the load torque of a ball screw?
- Thrust force × lead ÷ (2π × efficiency). A 50 kg table with μ = 0.1 on a 10 mm lead at 90 % efficiency needs about 0.087 N·m.
- Why does the tool say the stroke is too short?
- The accelerating and decelerating distance exceeds the stroke, so the entered speed is never reached and a triangular profile is used.
- Peak torque or RMS torque: which one sizes the motor?
- Both. Peak torque must stay inside the motor's instantaneous limit at that speed, and RMS torque below the rated continuous torque.