Figures of Merit (FM's) - stepper motor

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):

Now T=Kt I so