Electricity + Control September 2016

DRIVES, MOTORS + SWITCHGEAR

Velocity Velocity Torque Power

Time

Torque = Inertia X Acceleration Or T = J X α Where : α = Acceleration in radians/sec² J = Inertia in kg.metre²

Time

T = Torque in Newton.metres

Note that the Inertia is the sum of the motor rotor inertia plus the load inertia. Inertia for small systems are often expressed more conveni- ently in kg.cm² as this results more easily visualised numbers rather than tiny decimal numbers.

Time

S Curve

1 Newton.m² = (100)² kg.cm² = 10 000 kg.cm²

Time

Figure 3: Trapezoid move profiles.

During the plateau section (constant velocity) the torque is only required to overcome system friction. Finally, deceleration requires negative torque as deceleration is merely acceleration with a negative sign. At this point, the torque drops to zero in this example. This would not be true in the case of, say, a hoist which would have balance the torque produced by the mass of the load. Section C shows the resulting power produced by the motor. During acceleration the power produced rises linearly with the (con- stant) acceleration.

close the system down. This, of course should not occur in normal operation, and is dealt with in one of two ways: A power transistor can connect a high capacity power dump resistor across the smoothing capacitor to allow the excess energy to be dissipated as heat in the power dump resistor. When the volt- age across the smoothing capacitor reaches a safe level, the power dump is switched off. At the cost of considerable complexity the rectifier can reverse its action and pass the capacitor’s stored energy from right to left into the supply line. This is more efficient than the dissipative method using a power dump Which system is appropriate will depend on a number of factors. The power dump method is used in the power systems or sys- tems with a low duty cycle. For example, a payoff machine feeding wire from a stock drum into a batch packaging winder at constant tension would only be required to be in regeneration mode briefly at the end of each production cycle as it slowed the stock drum to zero speed. The rest of the cycle would see the drum at standstill or in motoring mode. A mine hoist, on the other hand, would spend a considerable amount of time in the regeneration mode as the cage or skip was being lowered. In this case a dissipative power dump would be a profligate waste of energy. ATrapezoid Move Figure 3 section A shows the principle of operation (velocity versus time). Themove commences with a period of acceleration at a constant rate. This is followed by a plateau section at constant velocity. Finally, this is followed by a controlled deceleration to complete the move. Section B shows the corresponding torque versus time. Note that the torque is constant during the acceleration and deceleration in this case. The relationship between torque, inertia and accelera- tion is given by:

Power = Torque X Velocity P = T ω where Power (P) is measured in Watts Torque (T) is measured in Newton metres Velocity ( ω ) is the angular velocity in radians/sec

More conveniently, ω can be expressed in Rev/sec or rev/minute.

Using ω in rev/sec P = 2 πω T ( ω in rev/sec) Using ω in rev/minute (RPM) P = 2 πω T ( ω in RPM) 60

If the torque is not zero after the move, as would be the case with a hoist, the power delivered by the motor is zero as there is no velocity. In practice, system losses will consume a small amount of power. This can be made zero by a brake fitted to the motor. Section D shows a modification to the trapezoidmove. The begin- ning and end of the acceleration and deceleration profile is modified to provide a gentle start and stop. This is the so-called S curve. When the load is driven by a gearbox with lost motion (backlash), the S curve reduces the acceleration jerk at the velocity transition points. Apart from reducing audible noise, gearbox life is extended. Move time is, of course, extended in this case.

September ‘16 Electricity+Control

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