Brake sizing calculator
Determine the required braking torque for two cases: static as a safety margin against a driving load torque (M_Br = M_Load·f_SB) and dynamic for decelerating a total inertia from a given speed to standstill within a set time (M_Br = J·ω/t + M_Load). The calculator also returns the braking energy per stop and the resulting permissible braking frequency, live with every input and with a traffic-light rating against a chosen braking torque.
Brake calculator
Model: ideal brake with constant braking torque, decelerating from n to 0 at constant angular deceleration. Friction-coefficient scatter, response and delay times, gear efficiency between brake and load, and thermal limit cases are not included and must be checked separately. Sizing tool, not a safety-related proof.
Results
Calculating …
Formulas and fundamentals
The static check secures holding against a driving load torque, for example on a lifting axis or an inclined drive. The required braking torque is M_Br,req = M_Load·f_SB, with the load torque M_Load at the brake and the required safety factor f_SB. Conversely, the available safety of a chosen braking torque is f_SB,avail = M_Br,avail/M_Load. Typical safety factors range from 1.5 to 2 depending on application and regulation, and higher where personal safety is involved.
The dynamic check sizes the brake for deceleration. From the initial speed n follows the angular frequency ω = 2π·n/60. To bring the total inertia J_tot referred to the brake from ω to zero within the braking time t, a deceleration torque M_a = J_tot·ω/t is needed. If a driving load torque acts at the same time, the brake must absorb it as well: M_Br,req = J_tot·ω/t + M_Load. A resisting load torque would instead reduce the required braking torque.
For thermal sizing the braking energy per stop matters: W_Br = ½·J·ω². This rotational energy is converted into friction heat during deceleration; a driving load torque over the braking distance adds to it. From the thermally permissible braking work per hour W_th/h,perm and W_Br follows the permissible braking frequency as stops per hour = W_th/h,perm / W_Br. In many applications this limits the cycle rate more strongly than the braking torque alone.
Worked example
Static: a driving load torque of M_Load = 25 Nm is to be held with a safety factor f_SB = 1.5. The required braking torque is M_Br,req = 25·1.5 = 37.5 Nm. A chosen brake with M_Br,avail = 50 Nm passes the check; its available safety is 50/25 = 2.0.
Dynamic: a total inertia J_tot = 0.15 kg·m² is to be decelerated from n = 1400 rpm to zero within t = 0.5 s, with no driving load torque. With ω = 2π·1400/60 = 146.6 rad/s this gives M_Br,req = 0.15·146.6/0.5 = 43.98 Nm.
The braking energy per stop is W_Br = ½·0.15·146.6² ≈ 1612 J. With a thermally permissible braking work of, say, 100,000 J per hour, the permissible braking frequency is about 62 stops per hour – above this rate the brake overheats even though the braking torque is sufficient.
Frequently asked questions
When do I use the static case, when the dynamic one?
Static when the brake must safely hold a stationary but driving load (holding brake on a lifting axis). Dynamic when it must actively decelerate a rotating mass (stopping brake). If a brake has to do both, run both checks and the larger required braking torque governs.
How do I choose the safety factor f_SB?
The factor covers friction-coefficient scatter, wear and uncertainty in the load torque. For holding brakes 1.5 to 2.0 is common; for passenger or load lifts and safety-related functions higher, often normatively prescribed values apply. The calculator uses the entered value unchanged.
Why does the dynamic braking torque rise with speed?
Because the deceleration torque M_a = J·ω/t is proportional to the angular frequency ω = 2π·n/60. Twice the speed means twice the deceleration torque for the same braking time. Shorter braking times increase it further, since t is in the denominator – an emergency stop with small t demands considerably more torque than a gentle stop.
Why does the braking frequency limit the brake on top of torque?
Each stop converts the energy W_Br = ½·J·ω² into heat. At a high cycle rate this heat accumulates faster than the brake can dissipate it. If the braking work per hour exceeds the thermally permissible limit, friction lining and brake overheat – regardless of whether the braking torque is sufficient. So besides torque, always check the thermal limit.
What is the difference between a driving and a resisting load torque?
A driving load torque (for example gravity on a lifting axis) acts in the direction of motion and must be absorbed by the brake as well – it increases the required braking torque. A resisting load torque (friction, process force) opposes the motion and would reduce it. The calculator adds the entered load torque; a resisting torque should conservatively be set to 0.
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