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 G_Н, and counterweight G_п:

G₀ = m₀ · 0,001·g;

G_н = m_н ·0,001·g;

G_п = m_п·0,001·g,

where G₀, G_н, G_п – measured in kN;

m₀, m_н, m_п – 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 force of friction 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 speed of descend is negative (less than zero) -V_H. 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 η_б and gear η_р defined by moments of rotation and power at the motor shaft and the drum shaft (at engine mode η_б і η_р are necessary to put in the denominator of formulas for М_с and Р_с, at generator mode η_б і η_р 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 С_к – rope stiffness, N/m;

Е_к – module of elasticity of the rope ТК6х19 during extension, N/mm², Е_к = 0,000172 N/mm²;

S_к- total area of rope cross-wire, mm² (Table 1.6);

l_к - length of cart rope branches, m (Figure 1.1, а) l_к=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=С_к·p²,

where С₁₂ – reduced rope rigidity, Nm/rad;

С_к – rope rigidity defined by the formula (1.2), N/m;

р=R_б/i_р – 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(I_Я) and ω=f(M) for d.c. motor. Electromechanical ω=f(I_Я) 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;

R_д – series resistance, Ohm;

R_яд = 1,32(R_я + R_дп + R_c) – resistance of the motor armature circle in a hot conditions, Ohm;

1,32 - temperature coefficient of resistance.

At R_д=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:

М_н = Р_н/ω_н,

where Р_н - nominal power of the motor, Wt;

ω_н – nominal speed of the motor, rad/s.

Additional resistance in the armature circle, which provides a given motor speed ω=0,5ω_н at І_я = І_н (М = М_н) 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; -S_Ke; -S_Ke/2; 0; S_H; S_Ke; 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 is taken for the engine mode and pluging mode (Fig. 1.5), "-" sign for generator (regenerating regime). In formulas (1.3) and (1.6)   

, .

Maximum moment of  generator (regenerating) mode

.

Calculating the properties of generating mode of induction motor in expression (1.3) we take  М_к = М_кг and the current values ​​of slip S and the critical slip are accepted as negative. Nominal moment and slip are determined by the following expressions:

,

where: Р_н – nominal capacity of the motor, Wt;

ω₀, ω_н–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, Hz.

1.3.9 For calculation of the artificial characteristics ω=f(І_Я) and ω= f(М) at first we must determine additional resistance R_д, which accordingly to the task provides motor speed ω=0,5ω_н at М = М_н. Additional resistance in rotor phase:

,

where R₂ – active resistance of the rotor phase, Ohm (Table. 1.3);

- artificial slip, relative units

S_н – nominal slip.

For calculation of artificial characteristics of induction motor we use formulas (1.3) and (1.4), in expression (1.3) we take S_к = S_u, 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 = U_н/I_н – total resistance of the armature circle of d.c. motor, Ohm;

- total resistance in the one phase of the induction motor rotor, Ohm;

І_п = к_п · І_н is starting current of the motor, А;

к_п is multiplicity of current overload, which is taken as equal to the multiplicity of moment overload (Table. 1.7);

R_p=R_яц= 1,32(R_я+R_дп+R_с) is internal resistance of the armature circuit of d.c. motor, Оhm (Table. 1.2);

R_p = R₂ is resistance of phase winding of the induction motor rotor, Ohm (table. 1.3);

І_н=І_2н – 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 R_1p 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 ω_с is speed of the motor defined by natural characteristic, rad/s;

D₆ – diameter of the drum, m;

і_р – gear-ratio of the reduction gear.

1.3.19 Plugging characteristic 2 (Fig. 1.6) is built by two points: (ω_с1;М_т1), (-ω₀; М=0). Initial moment at breaking М_т1 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 ω_с3 to the intersection 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 ω_н; М = М_с4).

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.