Equations For Selections; Load Torque During Constant Speed Running - Fuji Electric FRENIC-HVAC User Manual

3.1.3

Equations for selections

3.1.3.1

Load torque during constant speed running

[ 1 ] General equation
The frictional force acting on a horizontally moved load must be calculated. Calculation for driving a
load along a straight line with the motor is shown below.
Where the force to move a load linearly at constant speed υ (m/s) is F (N) and the motor speed for
driving this is N
M
60 F
υ
•
τ
=
•
M η
2 π
N
•
M
G
where, η is Reduction-gear efficiency.
G
When the inverter brakes the motor, efficiency works inversely, so the required motor torque should
be calculated as follows:
60 υ
•
τ
= F
• •
M
2 π
N
•
M
(60·υ) / (2π·N ) in the above equation is an equivalent turning radius corresponding to speed
M
υ (m/s) around the motor shaft.
The value F (N) in the above equations depends on the load type.
[ 2 ] Obtaining the required force F
Moving a load horizontally
A simplified mechanical configuration is assumed as shown in Figure 3.7. If the mass of the carrier
table is W (kg), the load is W (kg), and the friction coefficient of the ball screw is µ, then the friction
0
force F (N) is expressed as follows, which is equal to a required force for driving the load:
F = ( W + W ) g
• •
0
where, g is the gravity acceleration (≈ 9.8 (m/s
Then, the driving torque around the motor shaft is expressed as follows:
60 υ ( W
•
τ
=
•
M
2 π
N
•
M
(r/min), the required motor output torque τ
( N m )
•
η
( N m )
•
G
µ ( ) N
+ W ) g µ
• •
0 ( N m )
•
η
G
Figure 3.7 Moving a Load Horizontally
(N·m) is as follows:
M
2
)).
3-6
(3.1)
(3.2)
(3.3)
(3.4)