1.3 Methodical instructions
1.3.1 The fig.1.1, a should be used while defining the engine force on the reel rim. Beforehand the gravity of the cart G0, weight GН, and counterweight Gп:
G0 = m0 · 0,001·g;
Gн = mн ·0,001·g;
Gп = mп·0,001·g,
where G0, Gн, Gп – measured in kN;
m0, mн, mп – measured in kg;
g = 9,81 m/s2.
The parts of gravity force acting on the rope and the cart wheels, while ignoring the gravity of rope:
;
,
де
-
for
the loaded cart;
-
for
the empty cart.
The
total friction force of cart:
.
The
resultant
turning
effort
of
the drum:
.
The
"+"
at
Ft
is taken
at
lifting,
the
"-"
at going down,
that’s
because the
frictional
force
always
directed
against
the
direction
of
motion.
To
determine
the
mode
of
operation
of
electric
machine(generator
or
engine
mode),
speed sign should
be
considered.
We
accept
the
elevating
speed
greater
than
zero,
while
lowering
negative
(less
than
zero)
-VH.
Since
power
is
proportional
to
F·V,
then
at
the
same
signs
of
the
resulting
effort
F
and
velocity
of
cart
V
electric
machine
mode
will
be
the
engine
mode,
at
different
- generator
or
braking.
Preliminary
assessment
of
the electric
mode
to
properly
take
into account the
efficiency
of
the
drum ηб
and
gear
ηр
defined
by
moments
of
rotation and
power
at
the
motor shaft
and
the drum
shaft
(at
engine mode ηб
і ηр
are
necessary
to
put in the
denominator of formulas
for
Мс
and
Рс,
at
generator mode ηб
і ηр
are
set as multipliers).
1.3.2 Static moments of resistance on the drum shaft for different modes:
а)
engine
mode:
;
б)
generator mode:
.
1.3.3 Adduced to the motor shaft static moment of the mechanism:
а)
engine
mode:
;
б)
generator
mode:
.
1.3.4 Static power developing in the motor shaft:
а)
engine
mode:
;
б)
generator
mode
.
1.3.5 Total reduced to motor shaft inertia moment:
. (1.1)
1.3.6 Stiffness of the lifter rope branch is defined as:
, (1.2)
where Ск – rope stiffness, N/m;
Ек – module of elasticity of the rope ТК6х19 during extension, N/mm2, Ек = 0,000172 N/mm2;
Sк- total area of rope cross-wire, mm2 (Table 1.6);
lк - length of cart rope branches, m (Figure 1.1, а) lк=L+L1, lifting way L at the Table 2.1.
Assuming, that the rigidity of the shaft of motor, gearbox, drum and short counterweight L2 rope branch equal to infinity, the system of oblique lift electric drive can be considered as double-weight mechanical elastic medium (Fig. 1.2). Reduced to motor shaft cart rope branch rigidity can be calculated by the formula:
С12=Ск·p2,
where С12 – reduced rope rigidity, Nm/rad;
Ск – rope rigidity defined by the formula (1.2), N/m;
р=Rб/iр – reduced radius, m.
Block diagram of mechanical double-weight elastic medium without damping is shown in Fig. 1.3. Transfer function of double-weight mechanical elastic medium for control action:
,
where
- square
frequency
of
free
oscillations
of
double-weight mechanical elastic medium,
rad/s.
,
,
where
-
elastic moment on the
rope,
Nm.
1.3.7 Calculation of natural and artificial characteristics ω=f(IЯ) and ω=f(M) for d.c. motor. Electromechanical ω=f(IЯ) and mechanical ω=f(M) characteristics of d.c. motor correspondingly with an independent or parallel excitation are described by the following equations:
,
,
where
speed
of ideal idle running of the motor,
rad/s;
constant
at the
Ф = const;
-
total
resistance of armature circle,
Ohm;
Rд – series resistance, Ohm;
Rяд = 1,32(Rя + Rдп + Rc) – resistance of the motor armature circle in a hot conditions, Ohm;
1,32 - temperature coefficient of resistance.
At Rд=0 motor characteristic will be natural.
Natural and artificial characteristics for d.c. motor are constructed in Fig. 4.1 by two points. Nominal moment on the motor shaft is defined from the following expression, Nm:
Мн = Рн/ωн,
where Рн - nominal power of the motor, Wt;
ωн – nominal speed of the motor, rad/s.
Additional resistance in the armature circle, which provides a given motor speed ω=0,5ωн at Ія = Ін (М = Мн) is determined from the following expression::
,
where:
.
1.3.8 Natural ω=f(M) and artificial ω=f (І2) characteristics for induction motor with phase rotor are counted by the formula:
. (1.3)
For the natural characteristics
,
.
(1.4)
For the artificial characteristics:
.
Natural characteristics are calculated for the slip S:
-1; -0,7; -SKe; -SKe/2; 0; SH; SKe; 0,5; 1; 1,5; 2.
Critical slip for the natural characteristics:
.
. (1.5)
Critical slip for the artificial characteristics:
(1.6)
In the expressions (1.5) and (1.6) "+" sign are taken for the engine mode and plugging mode (Fig. 1.5), "-" sign for generator (regenerative regime). In formulas (1.3) and (1.6)
,
.
Maximum moment of generator (regenerative) mode
.
Calculating the properties of generating mode of induction motor in expression (1.3) we take Мк = Мкг and the current values of slip S and the critical slip are accepted as negative. Nominal moment and slip are determined from the following expressions:
,
where: Рн – nominal capacity of the motor, Wt;
ω0, ωн–correspondingly synchronous and nominal rotor speed, rad/s;
р – pole pair number of induction motor (Table 1.5);
f – the frequency of the source supply, Гц.
1.3.9 For calculation of the artificial characteristics ω=f(ІЯ) and ω= f(М) at first we must determine additional resistance Rд, which accordingly to the task provides motor speed ω=0,5ωн at М = Мн. Additional resistance int rotor phase:
,
where R2 – active resistance of the rotor phase, Ohm (Table. 1.3);
-
artificial
slip,
relative
units
Sн – nominal slip.
For calculation of artificial characteristics of induction motor we use formulas (1.3) and (1.4), in expression (1.3) we take Sк = Su, which is calculated by the formula (1.6).
Artificial characteristics ω=f(І2) and ω=f(М) are calculated for slips:
-1;-0,7; -0,3; 0; 0,2; 0,5; 0,7; 1; 1,5; 2.
1.3.10 At analytical calculation of resistances of the starting resistor at first we need to define coefficient λ:
,
where: m – given number of starting stages (Table. 1.7);
R1p = Uн/Iн – total resistance of the armature circle of d.c. motor, Ohm;
-
total
resistance in the one phase of the induction motor rotor,
Ohm;
Іп = кп · Ін is starting current of the motor, А;
кп is multiplicity of current overload, which taken as equal to the multiplicity of moment overload (Table. 1.7);
Rp=Rяц= 1,32(Rя+Rдп+Rс) is inner resistance of the armature circuit of d.c. motor, Оhm (Table. 1.2);
Rp = R2 is resistance of phase winding of the induction motor rotor, Ohm (table. 1.3);
Ін=І2н – nominal current of the induction motor rotor, А. (табл. 1.3)
1.3.11 Moment of the motor commutation
,
where
- starting
moment of the motor,
Nm.
1.3.12 Resistance of the stages of starting resistor
;
і т.д.
1.3.13 Resistance of sections of starting resistor
і
т.д.
1.3.14 Total resistance of starting resistor
1.3.15 Graphical calculation is when at first resistance R1p is calculated by nominal voltage and starting current.
1.3.16
Determination
of resistance value
(Fig. 1.6):
1.3.17 Then determination of resistance of sections and total resistance of starting resistor:
;
;
;
.
1.3.18 Speed of static movement of the cart, m/s:
,
where ωс is speed of the motor defined by natural characteristic, rad/s;
D6 – diameter of the drum, m;
ір – gear-ratio of the reduction gear.
1.3.19 Plugging characteristic 2 (Fig. 1.6) is built by two points: (ωс1;Мт1), (-ω0; М=0). Initial moment at breaking Мт1 is determined based on task variants (Table 1.7)
1.3.20
Resistances
of
plugging
stages
are determined in the graph
(fig.
1.6):
.
1.3.21
Resistance
of
plugging
sections
.
1.3.22
Initial
value
of
the
moment
during
lowering of the empty cart is defined from the graphical
constructions
(Fig.
1.6), building
ray 2'
in
parallel to the ray
2 and
horizontal line from the point ωс3
to
the intersiction with ray
2'. The
moment
is
used
in
the
next
task.
1.3.23 Characteristics of dynamic braking 3 (Fig. 1.6) for d.c. motor is built by two points:
(ω = 0; М = 0), (ω = 0,3 ωн; М = Мс4).
1.3.24
Resistance
of
dynamic
braking
for
d.c.
motor:
where
defined
from the
Fig.
6.1, previously
having draw ray
0К in
parallel to the natural characteristic
1.
1.3.25 Principle circuit for d.c. motor is shown in Fig. 1.7, for a.c. motor is shown in the Fig. 1.8.
Table 1.7 – Initial data in variants.
Variant number |
Motor type |
Performance accord to speed of rotating |
Amount of starting ratio |
Order of the maximal moment |
|
At startup КП=Мі/Мн |
At braking Кт=Мт.і/Мн |
||||
1 |
Д32 |
Low-speed |
3 |
2,5| |
2 |
2 |
МТН311-6 |
- |
3 |
2 |
2 |
3 |
Д32 |
Rapid |
3 |
2,5 |
1,8 |
4 |
МТН312-6 |
- |
3 |
2 |
1.8 |
5 |
Д41 |
Low-speed |
3 |
2,5 |
1.4 |
6 |
МТН411-6 |
- |
3 |
2 |
1.4 |
7 |
Д41 |
Rapid |
4 |
2,5 |
1,6 |
8 |
МТН412-6 |
- |
3 |
2 |
1,6 |
9 |
Д806 |
Low-speed |
3 |
2 |
1,8 |
10 |
МТН312-8 |
- |
3 |
2 |
1,8 |
11 |
Д806 |
Rapid |
5 |
2 |
2 |
12 |
МТН411-8 |
- |
4 |
2 |
2 |
13 |
Д808 |
Low-speed |
3 |
2,5 |
1,4 |
14 |
МТН412-8 |
- |
4 |
2 |
1,6 |
15 |
Д808 |
Rapid |
5 |
2 |
1,8 |
16 |
МТН511-8 |
- |
4 |
2 |
2 |
17 |
Д32 |
Low-speed |
4 |
2 |
1,6 |
18 |
МТН311-6 |
- |
4 |
2 |
1,8 |
19 |
Д32 |
Rapid |
4 |
2,5 |
1,4 |
20 |
МТН312-6 |
- |
4 |
2 |
2 |
21 |
Д41 |
Low-speed |
4 |
2 |
1,8 |
22 |
МТН411-6 |
- |
4 |
2 |
1,6 |
23 |
Д41 |
Rapid |
4 |
3 |
2 |
24 |
МТН412-6 |
- |
4 |
2 |
1,8 |
25 |
Д808 |
Low-speed |
4 |
2 |
1,8 |
Extension of the table 1.7.
Variant number |
Motor type |
Performance accord to speed of rotating |
Amount of starting ratio |
Order of the maximal moment |
|
At startup КП=Мі/Мн |
At braking Кт=Мт.і/Мн |
||||
26 |
Д32 |
Low-speed |
3 |
2,5| |
2 |
27 |
МТН311-6 |
- |
3 |
2 |
2 |
28 |
Д32 |
Rapid |
3 |
2,5 |
1,8 |
29 |
МТН312-6 |
- |
3 |
2 |
1.8 |
30 |
Д41 |
Low-speed |
3 |
2,5 |
1.4 |
31 |
МТН411-6 |
- |
3 |
2 |
1.4 |
32 |
Д41 |
Rapid |
4 |
2,5 |
1,6 |
33 |
МТН412-6 |
- |
3 |
2 |
1,6 |
34 |
Д806 |
Low-speed |
3 |
2 |
1,8 |
35 |
МТН312-8 |
- |
3 |
2 |
1,8 |
36 |
Д806 |
Rapid |
5 |
2 |
2 |
37 |
МТН411-8 |
- |
4 |
2 |
2 |
38 |
Д808 |
Low-speed |
3 |
2,5 |
1,4 |
39 |
МТН412-8 |
- |
4 |
2 |
1,6 |
40 |
Д808 |
Rapid |
5 |
2 |
1,8 |
41 |
МТН511-8 |
- |
4 |
2 |
2 |
42 |
Д32 |
Low-speed |
4 |
2 |
1,6 |
43 |
МТН311-6 |
- |
4 |
2 |
1,8 |
44 |
Д32 |
Rapid |
4 |
2,5 |
1,4 |
45 |
МТН312-6 |
- |
4 |
2 |
2 |
46 |
Д41 |
Low-speed |
4 |
2 |
1,8 |
47 |
МТН411-6 |
- |
4 |
2 |
1,6 |
48 |
Д41 |
Rapid |
4 |
3 |
2 |
49 |
МТН412-6 |
- |
4 |
2 |
1,8 |
50 |
Д808 |
Low-speed |
4 |
2 |
1,8 |
Figure 1.7 – Principal scheme of force part of d.c. electric drive.
Figure 1.8 – Principal scheme of force part of a.c. electric drive.