Inertia Matching Calculator
Reflected load inertia through a gear ratio, the motor:load ratio and the ideal gearing — rotary loads or leadscrew masses.
Gearing helps QUADRATICALLY: doubling the ratio quarters the reflected inertia — usually the cheapest fix for a sluggish, oscillating axis. Steppers tolerate mismatch poorly (keep ≤ ~5:1); modern servos with stiff couplings handle 10–30:1. The “ideal” ratio that matches 1:1 also maximises power transfer into accelerating the load.
Inertia Matching Calculator computes load inertia reflected through gearing and the motor:load inertia ratio — free, instant and private in your browser. Servo-system designers fixing sluggish, oscillating or over-tuned axes use it to skip the datasheet algebra: type your numbers, read the answer with the substituted formula shown step by step, and share an exact permalink of the calculation.
About Inertia Matching Calculator
Inertia Matching Calculator computes load inertia reflected through gearing and the motor:load inertia ratio using the standard engineering relation: J(reflected) = J(load)/N² + J(gearbox); linear mass: J = m·(lead/2π)²; ideal N = √(J(load)/J(motor)). Worked live: 120 kg·cm² of load through a 5:1 reducer reflects to just 4.8 + gearbox — a 3:1 ratio against a 1.5 kg·cm² rotor. The result recalculates on every keystroke, the worked-example panel shows your numbers substituted into the formula, and the Copy permalink button encodes the inputs in the URL so a colleague opens exactly your calculation. Everything runs client-side — nothing you type leaves your device.
How to use Inertia Matching Calculator
- 1Enter your values — the tool starts with realistic defaults for this exact use case, so the worked example is meaningful immediately.
- 2Read the live result and the worked-example panel, which substitutes your numbers into the formula step by step.
- 3Adjust any input to compare scenarios, then use Copy result or Copy permalink to share the calculation.
Why use Inertia Matching Calculator?
- ✓Implements the real formula — J(reflected) = J(load)/N² + J(gearbox) — with the substitution shown, not a black box
- ✓Built for servo-system designers fixing sluggish, oscillating or over-tuned axes
- ✓Copy result and permalink buttons — share the exact calculation in a README, forum answer or design review
- ✓100% free, no sign-up, runs entirely in your browser (works offline once loaded)
Frequently asked questions
How do you calculate inertia matching?+
Load inertia reflected through gearing and the motor:load inertia ratio follows J(reflected) = J(load)/N² + J(gearbox); linear mass: J = m·(lead/2π)²; ideal N = √(J(load)/J(motor)). For example, 120 kg·cm² of load through a 5:1 reducer reflects to just 4.8 + gearbox — a 3:1 ratio against a 1.5 kg·cm² rotor. The calculator applies the same relation and shows the substituted arithmetic so you can verify every step.
Why does my perfectly powerful servo oscillate?+
Torque was never the issue — inertia mismatch is. With a 50:1 load:rotor ratio the motor cannot impose its will between encoder samples, so gains must drop until response is mushy or hunting starts. Gear it down: reflected inertia falls with N².
What does 'inertia matching' (1:1) actually optimise?+
Maximum power transfer into accelerating the load — the same impedance-matching idea as electrical sources. You rarely need exactly 1:1; it marks the gearing around which acceleration performance peaks for a given motor.
Is the Inertia Matching Calculator free and private?+
Yes — completely free with no sign-up or usage limits, and it runs entirely in your browser: the values you enter are never uploaded or stored on a server.
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