Figures of merit (FM'S) are performance indices which give quantitative information on certain aspects of performance and design of actuators such as stepper motors. DC or AC servomotors etc.

**FIGURES OF MERIT (FM'S)**

Figures
of merit (FM'S) are performance indices which give quantitative information on
certain aspects of performance and design of actuators such as stepper motors.
DC or AC servomotors etc.

**1. Electrical Time constant (Te)**

Te=Lm/Rm
……….. (2.26)

where
Lm-Inductance of motor winding

Rm-resistance
of motor.

Te
governs the rate at which current rises when the motor winding is turned on.It
also determines how quickly the current decays when the winding is turned off.

In motion
control, the speed of response is of importance. Hence electrical time constant
Te must be minimized.

Te
dependent upon inductance and resistance of the motor winding. Inductance is
determined by magnetic circuit. (i.e.) magnet iron volume as well as volume of
copper used in the motor design. Once these have been designed, neither
reducing conductor size nor increasing the number of turns will reduce Te.
Otherwise magnetic circuit itself has to be redesigned.

**2. Motor time constant (Tm)**

Tm=J/(Ke.KtRm)=JRm/Ke ………… (2.27)

J-moment
of inertia of motor (kg-m2)

Rm-resistance
of the motor winding (Ω)

Ke-back
emf constant(volt s/ rad)

Kt-
torque constant (Nm/A)

Motor
back emf and torque constants are determined by magnetic circuit and phase
winding design. Winding resistance also from winding design. Moment of inertia
is determined by mechanical design.

In this
way motor time constant Tm combines all the three aspects of motor design viz,
magnetic circuit, electrical circuit and mechanical design. Achieving a low Tm
requires excellence in motor design. As a thumb rule the ratio of Te/Tm 0.1

Initial
Acceleration (a0):

A0=T/J(rad/S2)

Where
T-rated torque (N-M)

J-moment
of inertia(kg-m2)

a0 gives
a quantitative idea of how fast the motor accelerates to its final velocity or
position. Maximization of a0 calls for good magnetic circuit design to produce
high torque in conjunction with good mechanical design to minimize rotor
inertia. The moment of inertia of the load coupled to motor also determines a0.

**Motor Constant (km)**

km=T/√ ω

where T-
rated motor torque

ω -rated
power(w) of the motor

km=√Kt
Ke/Rm

This
shows that maximizing km causes minimizing R, maximizing Ke and Kt. Maximizing
Ke and Kt. Call for optimization of magnetic circuit design, decreasing
electrical time constant Te which is undesirable. A trade off between
electrical and magnetic circuit design is necessary to achieve a good km.

Power
rate (dP/dt):

Power
rate is (dP/dt)=(d/dt)(T.(dϴ /dt))=
T.(d2ϴ /dt2)=T.(T/J)=(T2/J) |
…..(2.28) |

Now T=Kt
I so

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