Answer Drives GT3000 - Application Notes; General Formulas Describing a Drive Operation

IMGT30017EN 53
5. APPLICATION NOTES
5A.1 General formulas describing a drive operation
M
U
L
I
L
L
I
D
, P
D
I
N
, A
N
U
N
P
M
η
inv
η
Μ
, cos ϕ
Μ
Rectifier
Inverter
Input
reactor
DC link
Capacitors
Figure 5A.2. One-line diagram of a drive with induction motor
NNN
IUA ⋅⋅= 3
A
N
= APPARENT DRIVE POWER
I
N
= DRIVE RATED OUTPUT CURRENT (RMS)
U
N
= DRIVE RATED OUTPUT VOLTAGE (RMS)
MMNM
AP ϕη cos⋅⋅=
P
M
= MECHANICAL POWER AVAILABLE AT MOTOR SHAFT
η
M
= MOTOR EFFICIENCY
COS φ
M
= MOTOR POWER FACTOR
invM
M
D
P
P
ηη ⋅
=
P
D
= POWER ON THE DC LINK
η
INV
= DRIVE EFFICIENCY
L
D
D
U
P
I
⋅
=
35.1
I
D
= AVERAGE CURRENT VALUE ON THE DC LINK
U
L
= INPUT VOLTAGE (RMS)
DL
II ⋅= 87.0
I
NPUT RMS CURRENT (ASSUMING A 3% INPUT REACTANCE)
DL
II ⋅= 25.1
I
NPUT RMS CURRENT (WITHOUT INPUT REACTANCE)
MMD
II ϕ cos32.1 ⋅⋅=
A
SSUMING η
INV
= 0.97
MML
II
ϕ
cos15.1 ⋅⋅=
I
NPUT RMS CURRENT (ASSUMING 3% INPUT REACTANCE & U
L
= U
N
)
MML
II
ϕ
cos65.1 ⋅⋅=
I
NPUT RMS CURRENT (ASSUMING 0% INPUT REACTANCE & U
L
= U
N
)
Table A5.3 Useful Conversion Factors
Category Multiply By to Obtain
Length meters
meters
inches
feet
millimeters
3.281
39.37
0.0254
0.3048
0.0394
feet
inches
meters
meters
inches
Torque Newton-meter
lb-ft
lb-in
lb-ft
0.7376
1.3558
0.0833
12.00
lb/ft
Newton-meter
lb-ft
lb-in
Rotation RPM
RPM
degrees/s
rad/s
6.00
0.1047
0.1667
9.549
degrees/s
rad/s
RPM
RPM
Moment of Inertia Newton-meters
2
oz-in
2
lb-in
2
slug-ft
2
oz-in-sec
2
lb-in-sec
2
2.42
0.000434
0.00694
32.17
0.1675
2.68
lb-ft
2
lb-ft
2
lb-ft
2
lb-ft
2
lb-ft
2
lb-ft
2
Power watts
lb-ft/min
hp
hp
BTU/hour
0.00134
0.0000303
746.00
33000.00
0.293
hp
hp
watts
lb-ft/min
watts
Temperature degree C = (degree F-32) x 5/9)
degree F = (degree C x 9/5) + 32