Servo Motor Sizing Calculator

This tool calculates three critical sizing parameters: (1) Inertia Ratio (load inertia reflected to motor shaft vs. motor inertia), (2) RMS Torque (root-mean-square torque over a duty cycle, essential for thermal rating), and (3) Regenerative Energy (energy returned to the drive during deceleration, important for brake resistor or regen-capable drive selection). These values help verify motor suitability before mechanical integration.

Use it early in motion system design—after defining your mechanical load and motion profile but before selecting a motor model. It’s especially valuable for CNC axes, robotic joints, rotary tables, and automated packaging machinery where precision, repeatability, and thermal stability are critical. Cross-check results with manufacturer datasheets before finalizing.

For rotating loads, calculate J_L using standard formulas (e.g., solid cylinder: J = ½mr²) and sum contributions from all components (couplings, belts, lead screws, payloads). For linear-to-rotary systems (e.g., belt drives or ball screws), reflect linear mass inertia using J_ref = m × (p/2π)², where p is pitch (m/rev). CAD software with mass properties or inertia measurement rigs can provide high-fidelity values.

A typical target is ≤10:1 (load-to-motor inertia ratio), though modern high-performance servos tolerate up to 30:1 with advanced tuning. Excessive ratios reduce stability, increase settling time, and amplify resonance—leading to overshoot or vibration. This calculator reflects load inertia through the gear ratio, so ensure your input gear ratio matches the actual mechanical reduction between motor and load.

Accel Time directly affects peak torque demand during startup and deceleration phases. Enter the *actual* time (in ms) the axis takes to reach max speed from rest—or conversely, to stop—under full acceleration/deceleration. Typical values range from 10 ms (high-dynamic pick-and-place) to 500+ ms (heavy industrial conveyors). Use motion profiling data or step-response measurements if available.

Duty Cycle is the percentage of time the motor is actively producing torque (not just powered on) within one complete operational cycle. Estimate by timing active motion vs. dwell/idle periods—for example, 3 seconds moving + 3 seconds stopped = 50% duty. Conservative estimates prevent undersizing; continuous operation requires 100% duty cycle evaluation for thermal limits.

First, verify inputs—especially Load Torque, acceleration time, and duty cycle—are realistic. If confirmed, consider increasing gear ratio (to reduce reflected load torque), reducing acceleration/deceleration rates, adding counterbalance, or selecting a higher-torque motor. Also check if intermittent overload capability (e.g., 150% for 60 s) covers peak demands without overheating.

Gear Ratio reduces reflected load inertia and torque but *increases* reflected speed—and since regenerative energy scales with kinetic energy (½Jω²), a higher gear ratio increases energy returned during deceleration. This is critical when using low-ratio direct-drive systems vs. high-ratio geared motors: always input the exact mechanical reduction to avoid underestimating brake resistor requirements.

No—this tool is specifically designed for closed-loop servo systems with continuous torque delivery and regeneration capability. Stepper motors lack feedback-based torque control, have different thermal behavior, and generally don’t regenerate energy. Use dedicated stepper sizing methods based on pull-out torque curves, acceleration torque margins, and microstepping losses.

Inputs use mixed practical units: Load Inertia in kg·cm² (standard in servo catalogs), Gear Ratio (dimensionless), Max Speed in RPM, Accel Time in ms, Load Torque in N·m, and Duty Cycle as %. Internally, the calculator converts to SI units (kg·m², rad/s, etc.) for physics-consistent results. Avoid unit mismatches—e.g., do not enter inertia in oz·in² without conversion.