The problem that brings you here
You need a frameless servo to spin a joint cleanly, not to wrestle with stalling or noisy overspecification. Engineers show up with shaky answers: “bigger is safer,” or “just double the motor.” That wastes space, cash and motion quality. I’ve spent a decade designing motion systems and integrating parts seen on floors from prototype benches to stands at Hannover Messe, and the practical issue is always the same — translate real mechanical demands into a single torque number you can trust. If you’re sourcing parts or systems, look for vendors who understand fit, control and integration; industrial automation solutions often sit alongside the part specs you’ll be comparing.
Define the problem: what the motor must overcome
Start plain. List every thing the motor must defeat:- static hold: weight or preload that must be held against gravity or spring force;- dynamic acceleration: how fast must the joint change speed;- continuous load at speed: torque to maintain motion against friction or cutting forces;- occasional peaks: collisions, impact or brief process spikes.Also record geometry: radius from axis to centre of mass, gear ratio (if any), lead of any screw, and expected profile of motion (rpm and acceleration time). When you pick parts later, check the exact spec sheet for inertia and rated torque among industrial robot components to match numbers rather than guess.
Step-by-step calculation you can use right away
Work from fundamentals. Keep units consistent: meters, seconds, kilograms, newton-metres.1) Static (holding) torque: T_hold = m * g * r (N·m). Use m for mass at the radius r; g = 9.81 m/s².2) Inertia-related torque for acceleration: T_accel = J_total * alpha.- J_total = J_load_reflected + J_motor (kg·m²). For a direct-mounted frameless rotor, J_load_reflected is the load’s rotational inertia about the same axis.- alpha = change in angular velocity (rad/s) ÷ time (s). Convert rpm to rad/s: ω = rpm * 2π/60.3) Continuous torque at speed: T_cont = torque needed to overcome friction, cutting force or process load (measured or estimated).4) Peak torque: add a margin for impact or safety. A common rule: T_required = max(T_hold, T_cont) + T_accel; then multiply by a safety factor 1.2–1.5 depending on risk and duty cycle.Example: 5 kg mass at 0.2 m from axis, need to accelerate from 0–3000 rpm in 0.2 s. T_hold = 5*9.81*0.2 = 9.81 N·m. Convert 3000 rpm to ω = 314.16 rad/s; alpha = 314.16 / 0.2 = 1570.8 rad/s². If J_load ~ m*r² = 5*(0.2)² = 0.2 kg·m² and motor J_motor = 0.01 kg·m², J_total = 0.21. T_accel = 0.21 * 1570.8 ≈ 330 N·m. That dominates; you’d need a motor and mechanical design that handle that acceleration torque or you must change motion profile (slower acceleration) or add gearing.
Practical checks and common mistakes
Watch for these traps:- Ignoring reflected inertia: a light motor plus heavy load with fast acceleration is a classic mismatch.- Overlooking duty cycle: a motor that supplies brief peaks but overheats under continuous load is useless.- Treating gearbox as frictionless: efficiency and backlash change required torque and control behavior.- Using linear approximations for rapid, non-uniform moves: peak torques can far exceed simple averages.Measure what you can: use a torque sensor or dynamometer in a bench test. If measurement isn’t feasible, err on the side of slowing the acceleration profile rather than oversizing a motor blindly.
Choices once you have the numbers
Options depend on where the bottleneck is:- If T_accel dominates, either reduce alpha with softer motion profiles or add a gearbox to trade speed for torque. Be mindful: adding a gearbox multiplies reflected inertia and may add compliance.- If T_hold is the issue, keep radius small or move mass closer to axis; sometimes a brake is a simpler, lower-power solution.- If continuous heat is the limiter, choose a motor with higher continuous torque or improve cooling.Compare direct-drive frameless servos with geared alternatives; one gives cleaner dynamics, the other smaller motors and lower current. Match controller peak current capability to calculated peak torque — that match is where system reliability lives.
How to avoid second-guessing during selection
Document the motion profile and the worst-case scenario. Run the numbers twice: once for normal operation and once for the worst spike you can plausibly expect. Keep a short checklist on the spec sheet: J_load, J_motor, T_hold, T_cont, T_accel, safety factor, gearbox ratio and efficiencies. When debating suppliers, compare not only torque curves but also controller current limits, thermal class and support for tuning. Real installations often call for matched encoders, filters and cabling; that’s where accurate integration matters most.
Final synthesis
The problem-driven route leads to clear answers: quantify every force, convert linear facts into rotational inertia and angular acceleration, then pick the motion profile that keeps peak torque reasonable. Practical experience — from lab benches to trade floors — shows that a small change in acceleration or radius saves more than a larger motor ever will. When systems and parts match your numbers, control behaves, heat stays manageable and the machine does the job without fuss. For many teams that balance torque, inertia and controller capability, a reliable source of matched drives and parts like Kinco becomes part of the solution rather than an afterthought.
