How to Calculate Magnetic Powder Brake Torque

How to calculate magnetic powder brake torque follows the same mechanical backbone as any tension component: the braking torque a unit must hold equals the web tension acting on the roll multiplied by the radius at which that tension acts. On an unwinder, the brake resists the pull of the web so the roll pays off at a controlled tension instead of free-spinning. Get this number right and you can size the brake, set its excitation current, and keep tension stable from a full roll down to the core. This guide covers the formula, a four-step method, two unwinding worked examples, and the slip-heat caveat that decides whether a brake survives continuous duty. If you are still deciding what a brake is for in your line, start with our explainer on what a magnetic powder brake is used for.

What "Torque" Means for a Magnetic Powder Brake

In a DIN-standard magnetic particle brake, the resisting torque is not made by friction pads you clamp — it comes from a magnetic field acting on fine powder held between the input and output members. The transmitted torque is set by the excitation current, and across the usable range it rises roughly in proportion to that current. For sizing, however, you do not begin with current; you begin with the mechanical job the brake must do, which is to hold a specific drag torque at the web so the unwinding roll cannot accelerate.

The Core Formula — Braking Torque Equals Tension Times Radius

Every brake torque calculation rests on one relationship:

• T = F × r
• T = required braking torque (newton-metres, N·m)
• F = web tension (newtons, N)
• r = effective roll radius (metres, m) at the point where tension acts

The same principle applies to unwinders, rewinders, and pull rolls. If your tension is in kgf and your radius in mm or cm, convert first: 1 N·m ≈ 10.2 kgf·cm, and 1 kgf ≈ 9.81 N. Mixing units is the most common reason a brake ends up undersized.

A roll shrinks as it unwinds, so the radius is never constant. You size the brake for the worst-case radius, which for an unwinder is the largest radius the machine will see — the full roll at the start of the run.

Step 1 — Determine Your Maximum Web Tension

Start from the tension your process needs. A tension controller or load cell in the line reports the actual running value; if you are designing from scratch, take the material width, the allowable tension per unit width for your film, paper, foil, or textile, and multiply. Write down the maximum tension F_max in newtons — the peak, not the average, because the brake must hold the peak without saturating.

Step 2 — Find the Operating Radius (and Why It Shrinks)

Measure the core radius and the full-roll radius of the roll being unwound. For a 3-inch (76 mm) core, r_core ≈ 0.038 m; for a full roll of 600 mm diameter, r_full ≈ 0.30 m. The brake sees its highest torque at the largest radius in its duty. On an unwinder that is the full roll at the start of the run, because the roll is biggest before any material has paid off.

Step 3 — Calculate the Required Brake Torque

Multiply your peak tension by the worst-case radius:

• T_required = F_max × r_max

If your line runs constant tension, this single number defines the brake's job. If tension varies by section, calculate T for each section and use the highest value. A web tension control system can then trim excitation current as the radius falls so tension stays flat from full roll to core.

Step 4 — Add a Safety Margin and Match the Rated Torque

Never pick a brake whose rated torque equals your calculated requirement exactly. Apply a typical safety margin of 1.2 to 1.5 times the calculated torque, then choose the nearest standard rated brake from the manufacturer's range. XW Machinery offers the DIN-standard magnetic particle brake, the ultra-thin magnetic particle brake for tight installations, and the hollow shaft magnetic particle brake for direct shaft mounting. The exact rated torque and torque–current curve for each model are printed on the nameplate and characteristic chart — use those, not a generic slope.

Worked Example A — Film Unwinding

A BOPP film line unwinds at a constant tension of 40 N. The core radius is 0.04 m and the full-roll radius is 0.30 m.

• T_required = 40 N × 0.30 m = 12.0 N·m
• With a 1.3× margin: 12.0 × 1.3 ≈ 15.6 N·m
• Select the next standard brake rated at or above ~16 N·m

Here an ultra-thin magnetic particle brake in the low-to-mid range is a good fit, and the miniature tension controller can reduce excitation current as the roll shrinks toward the core.

Worked Example B — Paper Unwinding

A paper unwinder runs at 180 N tension. The largest roll radius at the start of the run is 0.45 m.

• T_required = 180 N × 0.45 m = 81.0 N·m
• With a 1.3× margin: 81.0 × 1.3 ≈ 105.3 N·m
• Select a brake rated at or above ~105 N·m

For this duty a higher-rated unit from the magnetic powder clutches and brakes range, sized toward the top of the band, is appropriate, paired with a closed-loop controller that follows the radius down.

From Torque to Excitation Current (the Linear Slip Region)

Once you know the required torque, you set it with excitation current. Above the residual (slack) magnetization current, transmitted torque climbs roughly linearly with current until it reaches the rated value, after which it plateaus. The precise mapping lives on the model's characteristic curve — do not assume one brake's curve applies to another. If the brake cannot reach the needed torque at rated current, you have undersized it and must move up a frame size. The brake version of this math is the mirror of our magnetic powder clutch torque calculation, with the brake resisting on the unwind side instead of driving on the rewind side.

Don't Forget Slip Heat — Torque Is Not the Whole Story

A magnetic powder brake in tension control runs in continuous slip. The heat it must dissipate equals torque times slip speed:

• P_slip = T × ω_slip (watts = N·m × rad/s)

On an unwinder the brake rotor may turn slowly while the web moves fast, so the slip speed can be close to the web surface speed — which makes slip heat large even at modest torque. A brake that is torque-adequate but thermally undersized will overheat and lose torque. This is why duty cycle and cooling matter as much as the peak number. Read our brake overheating causes and solutions article before finalizing a high-slip application, and confirm the thermal rating with the manufacturer.

Common Calculation Mistakes to Avoid

• Using average tension instead of peak tension when sizing.
• Forgetting that radius changes through the run; always use the worst-case (largest) radius for an unwinder.
• Mixing units — keep everything in N and m, or convert cleanly.
• Sizing only for torque and ignoring slip heat in continuous-duty lines.
• Treating one model's torque–current curve as universal.

Brake vs Clutch — Why the Calculation Differs

A clutch and a brake share the T = F × r formula, but they sit on opposite sides of the web. The clutch drives or holds on the rewind side; the brake resists on the unwind side. Because an unwinder's roll starts large and shrinks, the brake's peak torque occurs at the beginning of the run, whereas a rewind clutch's peak torque occurs at the end. Size each for its own worst-case radius, and pair them through a shared web tension control system so tension stays matched across the machine.

Frequently Asked Questions

Can I size a brake from tension alone without the radius?

No. Torque is tension multiplied by radius, so without the roll radius the number is undefined. Even a fixed core adapter changes the effective radius, and you should confirm it against the brake selection method for your setup.

What if my tension varies during the run?

Calculate torque at the highest tension and largest radius combination your process reaches, then apply the safety margin. A closed-loop controller handles the variation between those limits by adjusting current as the roll unwinds.

How do I know the rated torque of a specific brake?

Read the nameplate or characteristic chart supplied with the unit. XW Machinery lists rated torque ranges on every magnetic particle brake product page.

Conclusion

Calculating magnetic powder brake torque is straightforward once you anchor on T = F × r, use the worst-case (largest) radius for an unwinder, apply a safety margin, and respect slip heat. Pair the math with the right brake and controller and you get stable tension from full roll to core. For help sizing a brake to your exact web, material, and duty cycle, contact XW Machinery and our engineers will recommend a rated torque and model from the magnetic powder clutches and brakes range.

Related Categories

• Magnetic Powder Brakes