Calculation
T'Br = JL · ωA/tR + TL
The required brake torque must not exceed the torque TBr actually produced by the brake.
T'Br = JL·ωA/tR + TL
Required brake torque
The required brake torque must not exceed the torque TBr actually produced by the brake.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Required brake torque T'Br — Minimum brake torque needed to reach the target braking time.
- Inertia to be braked JL — Inertia of all masses to be decelerated, referred to the brake shaft.
- Speed before braking nA — Operating speed immediately before the brake is applied.
- Required braking time tR — Time within which the shaft must be brought to a stop.
- Load torque TL — Additional acting torque; positive if it opposes braking, negative if it assists it.
Example
JL = 0.5 kg·m², nA = 1,500 rpm, tR = 2 s and TL = 5 N·m give T'Br ≈ 44.3 N·m.
Assumptions and limits
Uniform (linear) deceleration to a full stop (ωL0 = 0); constant load torque throughout the braking event.
Understand Required brake torque
This calculator determines the brake torque required to reach a target braking time, from the inertia to be decelerated, the initial speed and any acting load torque.
What does this quantity describe?
To decelerate a rotating mass with inertia JL from angular velocity ωA to a full stop within time tR, a brake torque of T'Br = JL·ωA/tR is required — plus any additionally acting load torque TL. The actually installed brake torque TBr must be at least this required value.
Think of a bicycle's brake torque: reducing the same speed in a shorter time needs a larger brake torque; a heavier wheel (larger inertia) also needs more brake torque for the same braking time.
Formula and variables
T'Br = JL · ωA/tR + TL
T'Br = JL · ωA/tR + TLJL = (T'Br−TL) · tR/ωAtR = JL · ωA / (T'Br−TL)
| Symbol / input | Meaning |
|---|---|
| Required brake torque T'Br | Minimum brake torque needed to reach the target braking time. |
| Inertia to be braked JL | Inertia of all masses to be decelerated, referred to the brake shaft. |
| Speed before braking nA | Operating speed immediately before the brake is applied. |
| Required braking time tR | Time within which the shaft must be brought to a stop. |
| Load torque TL | Additional acting torque; positive if it opposes braking, negative if it assists it. |
Choose the inputs correctly
JL is the inertia of all masses to be decelerated, referred to the brake shaft; nA the operating speed immediately before the brake is applied; tR the required braking time to a full stop; and TL an additionally acting torque (positive if it opposes braking, negative if it assists it).
How to use the calculator
Enter JL, nA, tR and TL to get the required brake torque T'Br. Then compare it against the torque TBr actually produced by the chosen brake.
Worked example
JL = 0.5 kg·m², nA = 1,500 rpm, tR = 2 s and TL = 5 N·m give T'Br ≈ 44.3 N·m.
Understand the result and units
T'Br ≈ 44.3 N·m is the minimum brake torque the chosen brake must supply to bring the shaft to a stop within 2 s. A brake with less torque would exceed the required braking time.
JL in kg·m², nA in rpm (converted internally to angular velocity), tR in s, TL and T'Br in N·m.
Sign convention for the load torque TL
TL is entered positive when it opposes braking — i.e. the brake must overcome it in addition to pure inertia (e.g. a driver that keeps pushing in the same direction while braking). TL is entered negative when it assists braking (e.g. a load that itself contributes to deceleration through gravity or friction). This convention applies consistently to both the required brake torque and braking time calculators and must be determined from the actual force direction in operation before entering values.
Typical applications
The formula is used when sizing service and safety brakes for drives with a defined braking-time requirement, such as elevators, cranes, machine tools and conveyors.
Assumptions, limits and common mistakes
The formula assumes uniform (linear) deceleration to a full stop. A time-varying brake torque (e.g. from fading friction due to heating) is not captured.
Common mistake: A common mistake is choosing the wrong sign for TL, or forgetting an additional torque that assists braking entirely, which would undersize the brake actually needed.
Frequently asked questions
What happens if TBr is smaller than T'Br?
The actual braking time will be longer than required; the brake is undersized for the required braking time.
How do I choose the sign of TL?
Positive if TL opposes braking; negative if TL assists braking.
Where do I get JL?
From the inertias of all rotating masses referred to the brake shaft, including the reduced inertia for multi-stage gear trains where applicable.
How does this relate to the braking-time calculator?
Both use the same base equation; here it is solved for T'Br, there for tR.
What's the next step after computing brake torque?
Use the friction-work calculator to check the heat energy released during a braking event, to estimate the brake's thermal load.