Calculation
W = 0.5 · TBr · ωA · tR
For frequent braking cycles, the hourly friction work (Wh = W·zh) must be checked against the brake's allowable continuous duty rating.
W = 0,5·TBr·ωA·tR
Braking friction work per stop
For frequent braking cycles, the hourly friction work (Wh = W·zh) must be checked against the brake's allowable continuous duty rating.
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Result
Select a target and calculate.
Understand the inputs
- Friction work W — Total energy converted to heat during one braking event.
- Brake torque TBr — Brake torque, assumed constant throughout the braking event.
- Speed before braking nA — Operating speed immediately before the brake is applied.
- Braking time tR — Time to a full stop, e.g. from the braking-time calculator.
Example
TBr = 45 N·m, nA = 1,500 rpm and tR = 3.49 s give W ≈ 12.3 kJ.
Assumptions and limits
Uniform (linear) deceleration to a full stop (ωL0 = 0); all kinetic energy is converted to friction heat in the brake.
Understand Braking friction work per stop
This calculator determines the friction work converted to heat during a single braking event from brake torque, initial speed and braking time — the decisive quantity for thermal brake design.
What does this quantity describe?
The friction work W = 0.5·TBr·ωA·tR equals the total rotational kinetic energy converted to heat during one braking event. For frequent braking cycles, the hourly friction work Wh = W·zh must additionally be checked against the brake's allowable continuous duty rating.
Think of a car's brake disc temperature during an emergency stop: the vehicle's entire kinetic energy is converted to heat at the brakes in a short moment — the more often this happens, the more total heat the brake must be able to dissipate.
Formula and variables
W = 0.5 · TBr · ωA · tR
W = 0.5 · TBr · ωA · tRTBr = W / (0.5 · ωA · tR)tR = W / (0.5 · TBr · ωA)
| Symbol / input | Meaning |
|---|---|
| Friction work W | Total energy converted to heat during one braking event. |
| Brake torque TBr | Brake torque, assumed constant throughout the braking event. |
| Speed before braking nA | Operating speed immediately before the brake is applied. |
| Braking time tR | Time to a full stop, e.g. from the braking-time calculator. |
Choose the inputs correctly
TBr is the brake torque, assumed constant throughout the braking event; nA the initial speed before braking; and tR the braking time to a full stop (e.g. from the braking-time calculator).
How to use the calculator
Enter TBr, nA and tR to get the friction work W released during one braking event.
Worked example
TBr = 45 N·m, nA = 1,500 rpm and tR = 3.49 s give W ≈ 12.3 kJ.
Understand the result and units
W ≈ 12.3 kJ is the total energy converted to heat during this one braking event. For repeated braking, Wh = W·zh (zh = cycles per hour) must be compared against the brake's allowable continuous duty rating Wh,allow.
TBr in N·m, nA in rpm (converted internally to angular velocity), tR in s; W results in joules or kilojoules.
Single friction work versus continuous duty rating
W describes the energy released during a single braking event and is compared against the allowable friction work per cycle Wzul. Under repeated cycling, however, heat load accumulates over time: Wh = W·zh, with zh the number of cycles per hour, must be checked against the allowable continuous duty rating Wh,allow specified by the brake manufacturer. A brake can be adequately sized for a single braking event yet still become thermally overloaded at too high a cycling frequency.
Typical applications
Friction work is the decisive quantity for thermal brake design under frequent cycling, such as on elevators, cranes and automated production lines with cyclic operation.
Assumptions, limits and common mistakes
The formula assumes uniform (linear) deceleration to a full stop and that all rotational kinetic energy is converted to friction heat in the brake, without accounting for other energy sinks.
Common mistake: A common mistake under frequent cycling is checking only the friction work of a single braking event without accounting for cycles per hour — only Wh = W·zh shows whether the brake's continuous duty rating is sufficient.
Frequently asked questions
What happens to the calculated friction work?
It is released as friction heat in the brake and must be dissipated by the brake's design (mass, cooling).
Is checking a single braking event enough?
Only for infrequent cycling; for frequent braking, Wh = W·zh must additionally be checked against the allowable continuous duty rating.
How does W relate to braking time?
W is directly proportional to tR at constant brake torque and speed; a longer braking time at the same torque means gentler deceleration, not automatically more friction work, since W primarily depends on TBr and ωA.
Where do I get the allowable friction work Wzul?
From the brake manufacturer's data, usually in tables such as TB 13-9 in Roloff/Matek.
What if W exceeds the allowable friction work?
Choose a larger or better-cooled brake, extend the braking time (if the application allows it), or reduce the speed or inertia to be braked.