Actuator Motor Sizing

Selecting a motor for a ball-screw linear actuator requires more than matching peak force. The full motion cycle matters: inertial torque during acceleration, RMS heating over repeated cycles, speed at the target stroke rate, and whether the rotor inertia is a sensible match for the load.

This calculator builds that full picture from your motion profile, load, axis orientation, screw geometry, and transmission, then evaluates every motor in the database against peak torque, RMS torque, and speed with a configurable safety factor.

1. Setting mode — Toggle Advanced to reveal additional parameters (friction, imbalance, screw efficiency, gear efficiency, gear inertia). In simple mode these are fixed at sensible defaults so you only need to set the essentials.
2. Motion Profile — Set stroke, peak velocity, acceleration, deceleration, and dwell time. The calculator computes the trapezoidal timing automatically, flags short-stroke triangular moves, and renders a live velocity diagram.
3. System — Choose Single Axis, 4-Actuator Platform, or 6-Actuator Stewart Platform. Multi-actuator modes distribute force per actuator, including the Stewart angle projection. Set Actuator Angle (Stewart only) for the cosine projection. Enable Holding Required if the actuator must support load at rest. Set the Safety Factor to scale all required values before motors are checked.
4. Load — Enter moving mass. In Advanced mode, also set friction force and an imbalance factor for uneven force sharing between actuators. Gravity acts on the full mass and is always included.
5. Ball Screw — Choose a common screw size (16 mm–32 mm, 5 mm or 10 mm lead) or enter custom pitch and diameter. Set screw length so mass and rotational inertia compute correctly. In Advanced mode, adjust efficiency for the screw’s mechanical losses (typically 85–95 %).
6. Transmission — Enable Auto Gear Ratio to let the calculator find the minimum ratio (in 0.5–5 ×) that keeps the load-to-motor inertia ratio ≤ 10:1 for each motor individually. Disable it to set a fixed ratio. In Advanced mode, add gear efficiency and drivetrain inertia for belt or gearbox reductions.
7. Results table — Sorted by pass → warn → fail, then by score. Re-sort by any column header. The Ratio column shows the effective gear ratio used per motor. Hover a row for a detailed breakdown of required vs. motor-rated torque, speed, power, load inertia, and total inertia. Use + Add custom motor to evaluate motors not in the built-in database — custom entries are saved to browser local storage.
8. Sharing — The full calculator state is encoded in the page URL automatically, so any configuration can be bookmarked or shared as a link.

• Force model — Static force (used during motion): F_static = m × g + F_friction. Holding force (used at rest): F_hold = m × g. Friction is excluded from holding because Coulomb friction is zero with no relative motion.
• Force distribution — Single axis: F × imbalance; 4-actuator: F/4 × imbalance; Stewart: F / (6 × cos(angle)) × imbalance. In simple mode the imbalance factor is fixed at 1.2.
• Screw torque — T_load = F × lead / (2π × η_screw × ratio × η_gear), where η_screw and η_gear are the screw and transmission efficiencies respectively.
• Peak torque is the maximum of |T_accel|, |T_const|, |T_decel|, and |T_hold|, where T_accel = T_load + J_total × α_accel and T_decel = T_load − J_total × α_decel.
• RMS torque represents thermal loading over the full move-and-dwell cycle: T_rms = √((T_accel² × t_accel + T_const² × t_const + T_decel² × t_decel + T_hold² × t_dwell) / t_total).
• Negative deceleration torque is valid regenerative behavior and still contributes to RMS heating through T².
• Inertia model — Load inertia reflected to the motor shaft: J_load = m × (lead / (2π × ratio))². Total inertia: J_total = J_motor + J_gear + J_screw / ratio² + J_load. The screw is modelled as a solid steel cylinder (density 7 850 kg/m³).
• Auto gear ratio uses binary search over [0.5, 5] to find the minimum ratio that satisfies J_load / J_motor ≤ 10. Each motor is evaluated with its own optimal ratio, so a low-inertia motor can run direct drive while a high-inertia motor gets geared.
• Status thresholds — fail if any margin is negative; warn if any margin is below 20 % or the inertia ratio exceeds 10:1; pass otherwise.
• Fit score (0–100) weighs RMS torque utilization (40 %), peak torque utilization (35 %), and speed utilization (25 %), then subtracts a penalty for inertia ratios above 10:1. Higher scores indicate better-matched motors; severely over-sized motors score lower.
• In Stewart mode, motion-profile inputs are actuator-axis values. The calculator applies angle-based load sharing but does not derive actuator travel from platform pose kinematics.