Formulary

Symbol

Unit

Definition

ω

[rad/s]

Angular velocity

Czk

[F]

Capacitance of the DC link capacitor

n

[1/min]

Motor speed

m

[kg]

Weight of the load

JI

[kgm²]

Load moment of inertia (can be reduced to the motor shaft)

Jm

[kgm²]

Motor moment of inertia

JI+m

[kgm²]

Mass moment of inertia of the load and the motor

Mbe

[Nm]

Acceleration torque

tbe

[s]

Acceleration time

PmeanAC

[W]

Mean acceleration power

Mbr

[Nm]

Braking torque

tbr

[s]

Deceleration time

PmeanBR

[W]

Mean braking power

Ebr

[Ws]

Braking energy

Perf

[W]

Required continuous power of the braking resistor

Ttotal

[s]

Total cycle time

i

[1]

Gear ratio

Ec

[Ws]

Energy that can be stored in the DC link capacitors

Epot

[Ws]

Potential energy of a load

Plower

[W]

Power required to reduce potential energy

tabsenk

[s]

Time during which the load is reduced

g

[m/s²]

Gravitational constant

h

[m]

Height at which the load is positioned / height difference of the lifting movement

Angular velocity:

Formulary 1:

Acceleration torque (from 0 → ω):

Formulary 2:

Braking torque (from ω → 0):

Formulary 3:

Mean drive power during the acceleration phase (from 0 → ω):

Formulary 4:

Mean drive power during the brake phase (from ω → 0):

Formulary 5:

Generated braking energy (from ω → 0):

Formulary 6:

If a gear unit is used, load inertia relating to the motor shaft is reduced by i².

Selecting the braking resistor:

The mean braking power of the individual braking operations must be considered in relation to the total cycle time.

Formulary 7:

Special case: lifting axes:

Formulary 8:

For vertical axes, in addition to the kinetic energy, the potential energy (caused by the mass) must be taken into account.

Behavior at standstill

The load is in the 1st quadrant. This means that no braking power occurs. The braking power only occurs in quadrants 2 and 4. When the load is lowered, the potential energy must be dissipated by the servo drive:

Formulary 9:

It depends on the respective height difference and the mass to be moved. The lowering time must also be taken into account for the calculation of the mean power.

Formulary 10:

Continuous power of the entire cycle

To calculate the cycle, the power for lowering and the remaining power values are included in the calculation.

Formulary 11: