Page 126 - Handbook of Electrical Engineering

108 HANDBOOK OF ELECTRICAL ENGINEERING

5.2.3 Load Torque versus Speed Characteristic

Most mechanical loads in the oil industry may be classified into two groups:-

• Quadratic torque versus speed.
• Constant torque versus speed.

A quadratic characteristic is typical of centrifugal pumps, centrifugal compressors, screw and
axial compressors, fans and turbo-machinery. The characteristic generally consists of two parts, a
static part and a dynamic part. The static part accounts for the initial torque that is required at
zero and very low speeds. When the driven shaft is stationary, or is rotating slowly, the lubrication
between the shaft surface or journal and its bearing is poor. About 5% to 15% of the full-load torque
is required to move the shaft. This initial torque is occasionally called ‘stiction’. As the shaft begins
to rotate this torque declines as the lubrication improves. Once the speed is above about 10% the
static torque can be ignored, since the shaft is well supported in its bearings by the lubricant. The
dynamic part of the torque is associated with the energy required to compress the fluid in the machine
and deliver it from its discharge port. The dynamic characteristic can be expressed in the form:-

T dynamic = KN 2 where N is the shaft speed

Most large centrifugal pumps and compressors are started in a ‘no-load’ state. This means
that the suction valve is open and the discharge valve is closed. The machine is filled with fluid but
there is little or no throughput of the fluid. The machine therefore requires the minimum energy and
torque from the motor. The full-speed torque for ‘no-load’ operation is between 40% and 60% of
the full-load operating torque. When the driven machine reaches full speed the discharge valve is
opened and the machine becomes fully loaded. The driven machine should not be allowed to operate
continuously in its start-up mode because the energy transmitted to the fluid will be rapidly converted
into heat. The machine could be thereby damaged. Small centrifugal pumps and compressors may be
started in a partly or fully loaded state. Starting the machine in a no-load state gives the advantage of
allowing the motor to create significantly more torque than the machine requires. The surplus torque
is able to accelerate the machine in the shortest possible time. The conventional induction motor has
only one rotor winding and has the torque characteristic already outlined. Such a motor is usually
adequate for driving centrifugal machinery. Figures 5.4, 5.5 and 5.6 show the complete curve for the
load torque of a centrifugal machine.
A constant torque versus speed characteristic is typical of reciprocating pumps, reciprocating
compressors, conveyors, lifting and cranage equipment and crushers. From zero to full speed the
torque is usually almost constant. In addition to high frictional and load torque, these systems may
also require a substantial accelerating torque due a high inertia being present. This type of machinery
may therefore be difficult to start and run up to full speed. The motor has to be carefully selected and
what is called a ‘double-cage’ motor may prove necessary. A double-cage motor has a rotor which
has two rotor windings, one on the outer surface as normal and one set deeper in the same or a
separate set of slots. The deeper winding is called the ‘inner winding’. By choosing different X-to-R
ratios for these two windings or cages it is possible for the motor to develop two torque characteristics
simultaneously for a particular slip. The combined torque can be almost constant during the run-up
period. However, it is still necessary to ensure that the motor develops adequate surplus torque to
accelerate the load when the terminal voltage is depressed.