Calculation formulas for BK.., BKB.., BP.., BR.., BY.., or BZ.. brakes

Static load torque at the motor shaft

Static load torque at the motor shaft

[M_L] = Nm

Static load torque at the motor shaft; application and gear unit efficiency are considered "aggravating".

[M_L] = Nm

Static load torque at the motor shaft; application and gear unit efficiency are considered "helpful".

[M_L,a] = Nm

Static load torque value at the output shaft, efficiency not considered

[η_L] = 1

Efficiency of the application

[η_G] = 1

Efficiency of the gear unit

[i] = 1

Gear unit ratio

1.1a

–

Checking the braking torque (holding function)

[M_4,100 °C] = Nm

Characteristic value of the static braking torque at 100 °C

[f_As] = 1

Static application factor

1.1b

–

Checking the braking torque (emergency stop function)

[M₁] = Nm

Characteristic value of the dynamic braking torque

[f_Ad] = 1

Dynamic application factor

1.2

Speed difference at brake application

[n_D] = min^-1

Change in motor speed until brake application

[t₂] = s

Brake application time; depending on the brake connection type, use t_2,I (AC) or t_2,II (AC/DC and DC)

[J_M] = kgm²

Motor mass moment of inertia with mount-on components, based on the motor shaft

[J_G] = kgm²

Mass moment of inertia of the gear unit, based on the motor shaft

[J_L] = kgm²

Mass moment of inertia of the application, based on the motor shaft

1.3

Calculation of emergency-stop speed

Calculation of emergency-stop speed

[n_EmergStop] = min^-1

Real emergency stop speed

[n_m] = min^-1

Relevant motor speed of the application

1.4a

Checking the maximum emergency-stop speed

[n_max,1] = min^-1

Maximum permitted emergency stop speed depending on the use case

1.4b

Checking the maximum operating speed

[n_Max,0] = min^-1

Maximum permitted operating speed of the brakemotor

1.5

Checking the no-load switching frequency

[Z] = h^-1

Required cycle switching frequency

[Z_B0] = h^-1

Maximum permitted no-load switching frequency of the brake

1.6

Calculation of maximum occurring braking work

Calculation of maximum occurring braking work

[W₁] = J

Maximum occurring braking work during emergency stop

1.7

Verifying if the braking work is within the maximum permitted braking work

[W_perm,n] = J

Maximum permitted braking work for emergency stop depending on the brake application speed

1.8

For BZ.. brakes: Determining the permitted emergency-stop switching frequency

[Z_B1] = h^-1

Permitted emergency-stop frequency (depending on the determined braking work)

[Z_B1max] = h^-1

Maximum permitted emergency-stop frequency for the selected load range

[W_per,T] = J×h^-1

Maximum permitted emergency-stop braking work within one hour

1.9

Calculation of the number of permitted emergency-stop braking operations until brake maintenance

[N_B2] = 1

Number of permitted emergency-stop braking operations until brake maintenance; observe the project planning notes.

[N_B2max ] = 1

Maximum permitted number of emergency-stop braking operations until end of service life

[W_insp] = J

Permitted braking work until brake inspection

[f_v] =1

Wear factor; determination in relation to the used load range for braking work

1.10

Calculation of the effective torque when braking (gear-unit output side)

Calculation of the effective torque when braking (gear-unit output side)

[M_{brake, output}] = Nm

Resulting gear unit load from the braking torque, based on gear unit output shaft

[η_G] = 1

Gear unit efficiency; for gear units with efficiency η_G < 90%, back-driving efficiency η_G' must be used (see formula 1.11)

[f_brake,output] = 1

Output design factor

1.11

Back-driving efficiency for gear units with efficiency η_G < 90%

[η_G'] = 1

Gear unit efficiency (back-driving)

[η_G] = 1

Gear unit efficiency

1.12

Checking the emergency stop load (torque)

[M_aEmerg.Off] = Nm

Maximum permitted emergency stop torque

1.13

Calculation of the effective gear unit radial force during braking

[F_{R, brake}] = N

Resulting gear unit load due to the radial force generated

[d₀] = mm

Diameter of the output shaft transmission element

[f_Z] = 1

Correction factor for the radial force (take into account any additional radial force due to the application, if applicable)

1.14

Verification of the emergency-stop load (radial force)

[F_RaEmerg.Off] = N

Maximum permitted emergency-stop radial force for the output shaft; applies when the point of force application is at the center of the shaft end, or at the face end in the case of hollow shafts

1.15

Calculation of the application’s emergency‑stop speed

[v_Emerg.Stop] = m × s^-1

Real speed at brake application

[v_L] = m × s^-1

Relevant speed of the load in the application at the point in time when the emergency stop is requested

1.16

Calculation of the typical maximum braking time

Calculation of the typical maximum braking time

[t_Bmax] = s

Maximum typical braking time

[f_Mmin] = 1

Braking torque reduction factor

1.17

Calculation of the typical maximum braking distance

[s_Bmax] = m

Maximum typical braking distance

[t_Bmax] = s

Maximum typical braking time

1.18

Calculation of the typical maximum stopping distance

[s_Amax] = m

Maximum typical stopping distance

[t_Signal] = s

System signal propagation time

1.19

1.19a) Calculation of the typical minimum braking time for gear units with η_G ≥ 90%

[t_Bmin] = s

Minimum typical braking time

[f_Mmax] = 1

Correction factor for braking torque

1.19b) Calculation of the typical minimum braking time for gear units with η_G < 90%

[t_Bmin] = s

Minimum typical braking time

[f_Mmax] = 1

Correction factor for braking torque

1.20

Calculation of the typical maximum deceleration when braking

[a_Bmax] = m × s^-2

Maximum typical deceleration when braking