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0066_Frame_C20 Page 51 Wednesday, January 9, 2002 5:49 PM

The operating speed of the motor will be fixed by the point at which the torque supplied by the motor
is just balanced by the torque requirements of the load. At any other condition, the motor and load will
be either accelerating or decelerating. Correct matching of a motor to a driven machine can only be
confidently accomplished if both the motor and the load torque–speed characteristics are known. The
motor torque–speed characteristics are usually provided by the supplier. The driven machine torque–speed
characteristics can be something of an enigma.
Friction devices like industrial sanders, buffers, and polishing machines have a torque–speed charac-
teristic that is initially very high, but drops sharply once motion is established. Continued acceleration
usually sees the torque requirement of the load decrease further but at a slower rate than that at start-
up. The difference between the static and dynamic friction accounts for this behavior.
Fans and blowers have a torque–speed characteristic that increases parabolically from zero as the speed
increases. Such machines do not, therefore, need much motor torque to enable them to start.
High inertia devices like machine tool drives, rolling mills, and electric lifts require a large torque on
start-up to overcome the inertia. Once motion is established the torque requirements tend to decrease
with increasing speed. The series-wound dc motors are ideal for these types of loads.
This brief discussion of rotating electrical machines is in no way comprehensive. A fuller discourse on
ac and dc machines is given both by Gray [1] and Sen [2]. Orthwein [3] presents an interesting practical
discussion on the mechanical applications of ac and dc motors and Kenjo & Nagamori [4] provide a
detailed in-depth study of permanent-magnet dc motors.

References

1. Gray, C. B. (1989), Electrical Machines and Drive Systems, Longmans Scientific and Technical, Harlow.
2. Sen, P. C. (1989), Principles of Electric Machines and Power Electronics, Wiley, Chichester.
3. Orthwein, W. (1990), Machine Component Design, West Publishing, St Paul, Minnesota.
4. Kenjo, T. & Nagamori, S. (1985), Permanent Magnet and Brushless dc Motors, Monographs in Electrical
& Electronic Engineering, Clarendon Press, Oxford.

20.3 Piezoelectric Actuators

Ramutis Bansevicius and Rymantas Tadas Tolocka

Piezoeffect Phenomenon

Piezoelectric effect was discovered by brothers Curie in 1880 [1]. The direct piezoelectric effect consists
in ability of certain materials to generate electric charge in proportion to externally applied force. The
inverse piezoelectric effect of these materials consists in their expansion under the action of electric field
parallel to the direction of polarization. Effects are lasting if force or electric field is acting. Effects have
been used for actuating/sensing functions in engineering applications.

Constitutive Equations

Coupled electric and mechanical constitutive equations of piezoelectric materials for one dimension
medium are

E
S = s T + dE (20.31)
T
D = ε E + dT (20.32)

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