POWER TRANSMISSION

Mechanical load characterization

MECHANICAL LOAD CHARACTERIZATION

A mechanical load may be decomposed in:

• an apparatus that has to be “moved” said apparatus load

• a transmission mechanism (gear train, gearbox) said transmission load

• the rotor of the motor said rotor load

Each of these parts has its own dynamic and static characteristic.

The apparatus load can be divided into two classes:

Dissipative load when energy supplied by the actuator is used to provide work e.g. tool machining like turning, milling etc. or lost for friction compensation e.g. industrial mixers or fans, rail drive, lifting.

Inertial load when energy supplied by the actuator is used to accelerate and/or to brake the load e.g. robots, high speed automatic positioning devices, metropolitan wheel drive

Load torque is usually widely variable during the appartus operations

Friction torque is function (proportional) of velocity

Moment of inertia almost constant

Dissipative load is characterized by the load torque and/or friction torque

Moment of inertia with relevant variations respect a nominal value

High speed

High accelerations (relevant jerk)

Dissipative torque may be considered a disturb of the system

Inertial load is characterized by the velocity and moment of inertia

Cm= J dω/dt + Cv + Ca + Cc

Ca static & dynamic (Coulomb) friction torqueCc load torque (and Power)

Cv = Fv · ω viscous friction torque (Bω)

J dω/dt = inertial load (Jα)

DYNAMIC LOAD CHARACTERIZATION

VERY SLOW DYNAMIC : J dω/dt << Cv + Ca + Cc

SLOW DYNAMIC : J dω/dt < Cv + Ca + Cc

FAST DYNAMIC : J dω/dt > Cv + Ca + Cc

VERY FAST DYNAMIC : J dω/dt >> Cv + Ca + Cc

POWER TRANSFER

For a gear train the load inertia can be reduced by a factor (N1/N2)² thus making the torque requirements of the actuator lower than driving the load directly.

Similarly, the inertia seen by the lead screw is also controllable by its coupling ratio

WHAT COUPLING RATIO SHOULD BE CHOSEN?

If the desired characteristic of the transmission is a speed or torque change ->

Coupling ratio chosen per the design specification

To minimize the energy dissipated by the actuator (electric motor) ->

Coupling ration chosen on the principle of an INERTIA MATCH

This concept uses the coupling ratio to make the reflected load inertia equal to the inertia of the motor; for a speed-reducing gear train one should choose the ratio N1/N2 by the formula:

N1/N2 = √J2/J1

Similarly, an optimal pitch for a lead screw which minimizes the energy dissipated

P= 2∏ √J1/M