Page 108 - Electric Drives and Electromechanical Systems

Chapter 3 Power transmission and sizing 101

The maximum load speed 300 rev min 1 a non-optimal gearbox with a ratio of 10:1
has been selected. The gearbox’s moment of inertia referred to its input shaft is
2
4.3 10 4 kg m .
The load’s moment of inertia has been determined to 5 10 2 kg m 2
The maximum load torque is 6 Nm.

Based on this information the minimum motor speed required can be determined
including an allowance for voltage fluctuations, in this calculation we use a safety factor of 1.2.
Motor speed ¼ 300 gear ratio 1:2 ¼ 3600 rev min 1

Continuous torque ¼ 0:6Nm
Consideration of the motor data provided by a manufacturer indicates that the following
motor and drive could meet the requirements.
Peak speed: 5000 rev min 1 10% at a terminal voltage of 95 V
Continuous stall torque: 1.2 Nm. Peak torque: 8.0 Nm
Voltage constant: 0.18 V s rad 1 Current constant: 0.18 Nm A 1
Moment of inertia: 1.7 10 4 kg m 2
Drive continuous current: 5 A Drive peak torque: 10 A
Drive voltage: 95 V
The required speed is below the peak motor speed of 5000 rev min 1 10%, and the
required torque is below the motor’s continuous torque rating. At the continuous torque
requirement, the motor requires 3.33 A, hence the selected drive is suitable.
To ensure that the motor-drive combination is acceptable, the acceleration can be
determined for the drives peak output of 10 A. At this current the torque generated by the motor
is 1.8 Nm, well within the motor rating. Assuming the worst-case situation of the external load
being applied during acceleration and using Eq. (2.12):
T peak T L =n 1:8 0:6 2
¼ ¼ 109:0 rad s
a L ¼ 2
I L 4 5 10
n I d þ 10 6 10 þ
n 2 10 2
Where I d is the inertia of the motor and gearbox, hence the load will be accelerated to its peak
speed of 300 rev min 1 within 0.5 s, which can be considered to be satisfactory. In practice the
acceleration rate would be controlled, so that the system, it particular any gearing, would not
experience significant shock loads.
nnn

3.8.2 Intermittent duty
When the acceleration performance is all important, the motor inertia must be consid-
ered, and the torque which is necessary to accelerate the total inertia must be determined
early in the sizing process. A suitable algorithm is as follows:

Using the application requirements and the required speed profile determine the
required speeds and acceleration.
Estimate the minimum motor torque for the application using Eq. (2.1).