The Linear Motor That Couldn’t Hold Position Under Load
We picked an ironless linear motor for a dispensing axis. The motor’s continuous force was 80 N. The dispensing load was 20 N. On the bench, it moved fast. On the machine, when the dispensing head pressed against the part (with 50 N side force), the motor lost position — it drifted. The problem: the ironless motor had no force at zero speed when the external load pushed against it. Wait, that’s not right — a linear motor holds position with current. The real issue: we sized for the continuous force (80 N) but didn’t account for the holding force needed when the axis was stationary under load. At standstill, the motor can deliver peak force (160 N) briefly, but continuous holding at 50 N requires current heating. The motor heated up and the drive derated. We switched to an iron-core motor with higher continuous force (150 N). The holding was stable. The mistake was not checking the continuous (thermal) force against the holding load.
Linear motor sizing is about the continuous force (thermal limit), not just the peak force. Ironless vs. iron-core is the first choice. This article covers the sizing.
Ironless vs. Iron-Core: The First Decision
Ironless (U-Channel) Linear Motor
The coil is a flat, ironless winding. No attraction to the magnet track. No cogging (smooth force). Light moving mass (high acceleration). But lower force density (needs a bigger motor for the same force).
Best for: High speed, smooth motion, low force (under 100 N), dispensing, scanning.
Iron-Core (Flat) Linear Motor
The coil has an iron core (laminations). Higher force density (more force per size). But it has attraction to the magnet track (normal force, 5–10× the thrust). And some cogging (force ripple). Heavier (lower acceleration).
Best for: High force (100–2000 N), heavy loads, machining, robotics.
| Type | Force Density | Cogging | Normal Force | Best For |
|---|---|---|---|---|
| Ironless (U-channel) | Low (50–200 N) | None (smooth) | Zero | High speed, dispensing, scanning |
| Iron-core (flat) | High (200–5000 N) | Some (can be reduced) | 5–10× thrust | Heavy loads, machining |
Step 1: Calculate the Required Force
The force the motor must deliver:
F = F_accel + F_friction + F_external
- F_accel: The force to accelerate the moving mass. F = m × a. For a 10 kg carriage at 5 m/s²: F = 50 N.
- F_friction: The friction of the linear guide. About 5–10 N (preloaded ball guides).
- F_external: Any process force (pressing, dispensing, cutting). 50 N for dispensing.
Total F = 50 + 10 + 50 = 110 N. The motor must deliver this force continuously (through the cycle).
Step 2: Continuous vs. Peak Force
The motor datasheet gives two force ratings:
- Continuous force (Fc): The force the motor can deliver indefinitely without overheating. This is the thermal limit (the motor heats up at this power).
- Peak force (Fp): The force the motor can deliver for a short time (1–2 seconds). Used for acceleration spikes. Can’t hold this continuously.
The motor that drifted under load was sized for peak (160 N) but the continuous force (80 N) was less than the 110 N average force. The motor heated up, and the drive derated the current. The holding force dropped.
Rule: the continuous force must exceed the cycle-average force. The peak force is for acceleration (brief). The continuous force is for the average load.
Step 3: Thermal (RMS) Force Calculation
The cycle has different forces at different times. The RMS (root mean square) force determines the heating:
F_rms = √[(F₁² × t₁ + F₂² × t₂ + …) / (t₁ + t₂ + …)]
For a cycle that accelerates (150 N for 0.1 s), cruises (20 N for 0.3 s), and presses (100 N for 0.5 s): F_rms = √[(150²×0.1 + 20²×0.3 + 100²×0.5) / (0.1+0.3+0.5)] = √[(2250 + 120 + 5000) / 0.9] = √[7370/0.9] = √8189 = 90.5 N.
The motor’s continuous force must exceed 90.5 N. An 80 N motor is undersized. A 120 N motor works.
The linear motor rule: Size for the RMS force (continuous, thermal limit), not the peak. The motor that lost position under load had enough peak force but not enough continuous force for the holding load. Calculate F_rms over the cycle. Pick a motor with continuous force > F_rms. Iron-core for high force, ironless for smooth/speed.
Step 4: The Magnet Track
The linear motor has two parts: the forcer (moving coil) and the magnet track (stationary magnets). The track length is the travel plus the forcer length. For a 500 mm travel with a 150 mm forcer, the track is 650 mm long.
The magnet track is expensive (neodymium magnets). Long tracks (over 2 m) add up. For long travels, multiple forcers can share one track.
Cooling: Natural vs. Forced
Linear motors generate heat (I²R in the coils). The heat goes into the machine frame. For high-duty cycles, add cooling.
- Natural convection: The forcer has a metal housing that dissipates heat to the air. For low-to-medium duty.
- Forced air (fan): A fan blows over the forcer. For medium duty.
- Water cooling: Channels in the forcer carry water. For high duty (continuous high force). Most expensive but allows 2× the continuous force.
For a dispensing axis (duty cycle 50%), natural cooling is fine. For a machining spindle (duty cycle 100% at high force), use water cooling.
Linear Motor vs. Ball Screw
| Criterion | Linear Motor | Ball Screw |
|---|---|---|
| Speed | Up to 5–10 m/s | Up to 1–2 m/s (critical speed) |
| Acceleration | Up to 10 g (low moving mass) | 1–2 g |
| Accuracy | ±0.001 mm (with linear encoder) | ±0.01–0.05 mm |
| Force | 50–5000 N | 1000–10000 N (more force) |
| Cost | High | Medium |
| Maintenance | None (no contact) | Lubrication, nut wear |
A Linear Motor Sizing Checklist
- What is the moving mass? (kg)
- What acceleration? (m/s² or g)
- What external process force? (N)
- F_accel = m × a. Friction. External force.
- What is the cycle? (Times at each force?)
- Calculate F_rms over the cycle.
- Ironless or iron-core? (Force and smoothness.)
- Continuous force > F_rms? (With margin.)
- Peak force > F_accel (max)?
- What travel length? (Magnet track.)
- Cooling? (Natural, fan, water?)
- Linear encoder on the load? (For position.)
The Bottom Line
Linear motor sizing is the RMS force (thermal limit), not the peak. The motor that drifted under load had enough peak force but not enough continuous force for the holding load. Calculate F_rms over the cycle. Pick an ironless motor for speed and smoothness, an iron-core motor for high force. Add water cooling for high-duty cycles. The axis that holds position under load wasn’t the highest-peak motor — it had the continuous (thermal) force for the cycle.
