Calculation
tR = JL · ωA / (TBr − TL)
A larger brake torque or a smaller inertia shortens braking time; a load torque that assists braking shortens it further.
tR = JL·ωA/(TBr−TL)
Required braking time
A larger brake torque or a smaller inertia shortens braking time; a load torque that assists braking shortens it further.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Braking time tR — Time to a full stop with the available brake torque TBr.
- 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.
- Available brake torque TBr — Brake torque actually produced by the brake.
- 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, TBr = 45 N·m and TL = 5 N·m give tR ≈ 1.96 s.
Assumptions and limits
Uniform (linear) deceleration to a full stop (ωL0 = 0); constant brake torque and load torque throughout the event.
Understand Required braking time
This calculator determines the time to a full stop from the available brake torque, the inertia to be decelerated, the initial speed and any acting load torque.
What does this quantity describe?
The braking time tR = JL·ωA/(TBr−TL) follows the same base equation as required brake torque, solved here for time instead. A larger available brake torque TBr or a smaller inertia JL shortens braking time; a load torque that assists braking (TL negative) shortens it further.
Think of braking a loaded shopping cart: with the same braking force, an empty cart stops faster than a fully loaded one — likewise, a smaller inertia shortens braking time for the same brake torque.
Formula and variables
tR = JL · ωA / (TBr − TL)
tR = JL · ωA / (TBr−TL)TBr = JL · ωA/tR + TLJL = tR · (TBr−TL) / ωA
| Symbol / input | Meaning |
|---|---|
| Braking time tR | Time to a full stop with the available brake torque TBr. |
| 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. |
| Available brake torque TBr | Brake torque actually produced by the brake. |
| Load torque TL | Additional acting torque; positive if it opposes braking, negative if it assists it. |
Choose the inputs correctly
JL is the inertia to be braked, nA the initial speed before braking, TBr the brake torque actually produced by the brake, and TL an additionally acting torque (positive if it opposes braking, negative if it assists it).
How to use the calculator
Enter JL, nA, TBr and TL to get the resulting braking time tR.
Worked example
JL = 0.5 kg·m², nA = 1,500 rpm, TBr = 45 N·m and TL = 5 N·m give tR ≈ 1.96 s.
Understand the result and units
tR ≈ 1.96 s is the time needed to decelerate the shaft from 1,500 rpm to a stop with the given brake torque TBr. If a shorter braking time is required, either TBr must be increased or JL reduced.
JL in kg·m², nA in rpm (converted internally to angular velocity), TBr and TL in N·m; tR results in seconds.
Cross-checking against the brake-torque calculator
Since both calculators rest on the same equation TBr = JL·ωA/tR + TL, the result is easy to cross-check: plugging the braking time tR computed here back into the brake-torque calculator with the same JL, nA and TL must reproduce exactly the original TBr. This cross-check is useful for catching input mistakes or a wrong sign on TL early.
Typical applications
The formula is used to find the resulting braking time for an already-selected or existing brake and compare it against a required braking time, e.g. for retrofits or comparing brake alternatives.
Assumptions, limits and common mistakes
The formula assumes uniform (linear) deceleration to a full stop, with constant brake torque and load torque throughout the braking event.
Common mistake: A common mistake is confusing TBr with T'Br (required brake torque) — here the calculation uses the actually available torque of an already chosen brake, not a target value.
Frequently asked questions
What's the difference between TBr and T'Br?
TBr is the torque an already-chosen brake actually produces; T'Br is the minimum torque computed as required for a target braking time.
How do I shorten the braking time?
A larger brake torque TBr, a smaller inertia to be braked JL, or a load torque that assists braking (entered negative) all shorten tR.
What if TBr is smaller than TL?
Then the denominator becomes negative and no physically meaningful braking time results — the brake cannot decelerate the load against the acting opposing torque.
Can I use this for sizing too?
For forward sizing, the required brake torque calculator is better suited; this calculator is more for verifying an already-chosen brake.
What comes after computing braking time?
Use the friction-work calculator to estimate the heat energy released over this braking time and thus the brake's thermal load.