Page 112 - Electric Drives and Electromechanical Systems

Chapter 3 Power transmission and sizing 105

force and any continuous force which is present during acceleration. If this is not
achievable, a different motor will be required.
The motor’s root-mean-square (r.m.s.) torque requirement can then be calculated
as a weighted time average, in addition this will allow the motor’s temperature rise
to be estimated.

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Example 3.7
Determine the size of the linear motor, and drive required to move a mass of 40 kg, a distance
of 750 mm in 400 ms.
The system has a dwell time 300 ms, before the cycle repeats.
Assume that the speed profile is trapezoidal, and equal times are spent accelerating,
decelerating and at constant speed.
Assume the frictional force is 3 N.
1
1
The motor’s parameters are: force constant of 40 NA , back emf constant of 50 V m s,
winding resistance of 2 U and thermal resistance of the coil assembly, 0.15 CW 1

The acceleration and peak speed can be determined using the process determined in
Section 2.6, hence
3d 1
_ x ¼ ¼ 2:81 m s
2t m
and
3 _ x
€ x ¼ ¼ 21:09 m s 2
t m
The acceleration force required is given by
F a ¼ M L € x þ F f ¼ 846 N

This now allows the calculation of the root mean square force requirement
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2
2t m F þ t m F 2 f
a
F rms ¼ ¼ 519 N
t m þ t d
The drives current and voltage requirements can therefore be calculated
F a
I peak ¼ ¼ 21:2A
K F
V drive ¼ _ xK emf þ I peak R w ¼ 183 V