Variable speed drives for asynchron asynchronous ous motors motors
1
Altivar 71 Option: braking units and resistors Determining the braking unit and resistor Calculating the various braking powers makes it possible to determine the braking unit and the braking resistor. Presentation of the two main types of operation: A and B A The braking power during deceleration is characterized by a peak power Pf obtained obtained at the start of deceleration, which decreases to 0 in proportion with the speed. Example: Stopping centrifuges, translational movement, change of direction, direction, etc
B Braking power at constant speed n 2. Example: Vertical downward movement, motor/generator test bench, gravity conveyors, etc.
>
n1 n2 Tl Tb ˆ
Pb
Motor speed Motor speed during deceleration Load torque Braking torque Maximum braking power
[rpm] [rpm] [N m ] [N m ] [ W]
Pb
Average braking power during time tb
[W]
tb
Braking time
[s]
n +n 1
n n1
tb
0 0
t
tb
-n
t
2
Tl
T
tb
Tl
t Tb
t Pbraking
tb
Pbraking
t t
Pb Pb
Pb
Note: These two types of operation can be combined. Type A operation Calculating the braking time from the inertia. tb
J⋅ω
= -----------------Tb + Tr
ω
2π ⋅ n 60
Tb
= --------------
Σ ⋅(
)
J n 3 – n 4 = ----------------------------------
ˆ P b
9 , 55 ⋅ t b
Pb Tb ∑J n n3 n4 tb ˆ P b
Motor braking torque Total inertia applied to the motor Motor speed Motor speed ahead of gearbox Motor speed after gearbox Braking time Peak braking power
[Nm] [kgm2] [rpm] [rpm] [rpm] [s] [W]
Pb
Average braking power during time tb
[W]
Tr
Resistive torque
[N m ]
Motor
Gearbox
n3
60288-EN_Ver2.1.fm/8
References: pages 60288/3 and 60288/5
n4
i=
Japplied =
Characteristics: pages 60288/2 and 60288/4
9,55
n3 n4
Jmachine i
2
Dimensions: pages 60294/12 and 60294/13
Schemes: page 60295/8
ˆ P b 2
= ------
Machine
∑ J = Jmotor +Japplied
Presentation: pages 60288/2 and 60288/4
T b ⋅ n3
= ----------------
Selection (continued)
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Variable speed drives for asynchronous motors
1
Altivar 71 Option: braking units and resistors
Type B operation 1
W m v tb ˆ P b
Kinetic energy Weight Speed Braking time Peak braking power
[Joule] [kg] [m/s] [s] [W]
Pb
Average braking power during time tb
[W]
Tb
Braking torque
[Nm]
n
Motor speed
[rpm]
g a v
Acceleration Deceleration Linear downward speed
9.81 m/s2 [m/s2] [m/s]
J
ω
Moment of inertia Angular speed
[kgms2] [rad/s]
tb
Downward stopping time
[s]
Braking power of a load moving horizontally with constant deceleration (e.g.: carriage)
m⋅v 2
W
2
Pb
W tb
ˆ P b
= -----
=
Pb ⋅ 2
Braking power for an active load (e.g.: test bench)
Tb ⋅ n
Pb
3
2
= ---------------
= --------------
9,95
Braking power for a downward vertical movement
Pb
ˆ P b
m⋅g⋅v
=
2
=
J⋅ω m ⋅ ( g + a ) ⋅ v + -------------tf
ω
2π ⋅ n 60
= --------------
All the braking power calculations are only true if it is assumed that there are no losses (η = 1) and that there is no resistive torque. To be even more precise, the following must be considered: b the losses and the resistive torque of the system, which reduce the necessary braking power b the driving torque (the wind, for example) which increases the braking power The required braking power is calculated as follows: ˆ P bR
Maximum actual braking power
[W]
PbR
Continuous actual braking power
[W]
ηtotal
Total efficiency Braking power connected with the resistive or [W] driving torque (not taken into account in the calculation). Pload can be positive or negative. Drive efficiency = 0.98 Mechanical efficiency Motor efficiency
Pload
ηdrive ηmec ηmot
Udc
Braking unit engage threshold
[V]
ˆ P bR
ηtotal
=
( Pˆb – P load ) × η total
PbR
=
( P b – P load ) × η total
η me c × η mo t × 0,98
For braking, the value of the braking r esistor is selected to match the required power and the braking cycle. In general: ˆ P bR
tc
=
2
2
U dc ⇒R R
= --------------
U dc
= -------------ˆ
P bR
Cycle time U pw ard braking pow er, therefore zero
[s] [W]
Continuous power is obtained by taking the operating cycle into account.
Rise time Average braking power during downward movement
The braking unit is selected taking the following into account: b the continuous power P f1 b the average braking power during downward movement P f2 ˆ b the peak power P f . Depending on these elements, select the braking unit according to the characteristics on page 60288/2. The braking resistor is selected taking account of the same elements listed above, but with the addition of a check to ensure 2 dc ⎞ -------------- . that t he resist ance value wil l all ow the peak power to be exceeded ⎛⎝ R = U ⎠ ˆ Pf
Note: The resistance value must always be greater than or equal to the values given in the tables on pages 60288/4 and 60288/6.
