Control questions

1. Name basic parts of generator and specify their purpose.

2. What does a value depend on EMF generator of direct-current?

3. Name the conditions of selfexcitation of generator of parallel excitation.

4. What basic equations do they determine properties of generator of direct-current?

5. What reasons do cause the decrease of generator voltage of parallel excitation at the increase of load?

6. Name characteristic points on external characteristic of generator of parallel excitation.

7. What consequences for the generator of parallel excitation can have a short circuit of load?

8. By what methods it is possible to regulate generator voltage of parallel excitation at the change of load?

 

Laboratory work3

RESEARCH OF DIRECT CURRENT МОТОRS

Aim of work

Acquaintance with the methods of experimental research and properties of direct current motors with the parallel and seriesexcitation.

Theory

Electric motor is converter of electric energy which is brought from the external electric network, into the mechanical energy of motor shaft.

Unlike generator, the direct motor load is been by the mechanical moment M_mh, which counteracts to the rotor rotation. Current of armature circuit depends on the degree of load.

The electromagnetic moment of direct current motor, as well as generator, is created as a result of co-operation of armature current with the magnetic flux of air-gap, but in motor this moment assists to the rotation of rotor, while in generator it counteracts to the rotation.

During the motor rotor rotation there is EMF in the armature winding, which has the same physical nature that the EMF of generator armature winding, but in motor this EMF counteracts to passing of current through the armature winding and is called back (counter) emf (E). Therefore the equation of electric equilibrium in the direct current motor armature winding has a kind:

U = E + I_armR_arm = C_eΩФ+ R_armI_arm; (3.1)

Physical maintenance of equation (3.1) is very simple: voltage of external network must be such, that to balance back (counter) emf action and voltage drop in the armature winding.

In the nominal mode of operations about 90% of voltage, supplied with armature, is counterbalanced by back (counter) emf. At the ideal open circuit (when resulting load moment at the rotor shaft equals a zero) all supplied voltage is fully counterbalanced by back (counter) emf and angular speed of rotor rotation equals to:

Ω₀ = U/C_eФ

The real motor even at open circuit (o.c.) has on the shaft a small moment of resistance M_o, conditioned by air friction of rotor, by bearing friction, by commutator friction, and also other losses of energy at idling. Therefore the current of motor armature winding is though small, but does not equal to zero.

The motor electromagnetic moment M_em can be defined mathematically as a ratio of electromagnetic power P_em =І_armЕ to angular rotation speed Ω, that is:

M_em = P_em/Ω = EI_arm/Ω = C_eΩФI_arm/Ω = C_eФI_arm. (3.2)

Practically often in place of angular rotation speed Ω they use frequency of rotation “n”, which is measured in RPM. Then the equation (3.2) adopts a kind:

M_em = C_M ∙I_arm∙Ф (3.3)

where С_м =2π С_е /60 − coefficient of moment.

Further will consider, that the rotor rotation is characterized by angular frequency Ω and then С_м = С_е.

For the system "motor - load", as well as for any mechanical system, under second law of mechanics we have:

M_M – M_br = J∙dΩ/dt (3.4)

where M_M – turning moment of motor; M_br - brake moment of load; J – moment of inertia of the system, reduced to the motor shaft; dΩ/dt – angular acceleration.

From equation (3.4)follows, that in the stable mode of operations the turning moment of motor equals to a brake moment. For simplification they consider, that the turning moment of motor equals to its electromagnetic moment and thus, is determined by formula (5.2).

Operating characteristics of motors may be natural, artificial and performance. Natural characteristics are examined at condition that the parameters of motor and network have basic values.

Artificial characteristics are examined at condition that some parameters of motor or parameters of network are artificially changed. Performance characteristics depend on motor operating conditions, for example, temperature, power of source and etc

We will consider only two characteristics of direct current motor with the parallel and series excitation: speed-torque characteristic and torque characteristic.

Dependence of rotation frequency Ω on load torque M in the stable mode of operations is called speed-torque characteristic: Ω = f(М) at U = const.

Dependence of torque (or electromagnetic moment) on the armature current at the U = const is called torque characteristic. For motor with the parallel excitation from formulas (3.1) and (3.2) we have: Ω = (U/C_eФ) – R_armI_arm/C_eФ; I = M/C_eФ; (3.5)

Putting lower equation of the system (3.5) in upper one’s, we will get equation of speed-torque characteristic of direct current motor with the parallel excitation.

(3.6)

Equation (3.6) at condition that magnetic flux Ф saves its сonstant value (because U = const), shows, that speed-torque characteristic is falling straight line (fig. 3.1).

Will find a point of intersection with the abscissas axis from equation (3.6), taking Ω =0, that corresponds to the mode of motor starting. Then the initial starting torque M_st equals to:

(5.7)

where I_st = U / R_arm – initial starting current.

Initial starting current I_st of motor with the parallel excitation is much more a nominal current of armature winding, because resistance of motor armature winding is very small, and in the moment of starting a back (counter) emf Е = С_е ΩФis absent, as Ω = 0.

As possible to see, the initial starting current does not depend on that, a motor starts at load, or at idling.

As follows from equation (3.7), direct current motor as a result of large value of initial starting current, also has enough large initial starting torque. This is by the considerable advantage of direct current motor on comparison, for example, with the asynchronous motors of alternating current.

Under action of initial starting torque the motor multiplies frequency of rotation enough quickly, back (counter) emf grows as a result, that causes reduction of current in the armature circuit and the proper reduction of a torque. As soon as the torque will be balanced by the brake moment M_br, current of the armature І_arm and frequency of rotation Ω will attain the stable values (fig. 3.1). Mechanical power appears on the motor shaft: P_mh = M_br∙Ω₁. Fig. 3.1

Thus, unlike the initial starting current, stable value of armature current depends on load: I_arm = M_br / C_eФ.

The larger motor load, the greater armature current and the larger influence of demagnetizing armature reaction on the magnetic flux in air-gap. Owing to, speed-torque characteristic in area of the large load deviates from line, that it is shown on the fig. 3.1 by dotted line.

Torque characteristic of direct current motor with the parallel excitation must have according to equation (3.3) the form of straight line that goes out from the beginning of co-ordinates, but as a result of demagnetizing armature reaction in area of large values of current it deviates from line (fig. 3.2).

The direct current motor with the independent excitation has the same characteristics, as well as motor with the parallel excitation. It is needed to mark, that in the small range of change of load moment the speed of rotor rotation of motors with the parallel and independent excitation changes insignificantly. Such speed-torque characteristics are called hard. Fig. 3.2

Now we will consider speed-torque and torque characteristics of direct current motor with the series excitation, the chart of which is represented on fig.3.3.

In such motor an armature current is by the excitation current simultaneously, that is Fig. 3.3 І_arm = I_ew. Considering, that magnetic flux is proportional to the current of excitation Ф = KІ_arm, and, putting this expression in formula (5.3), we will get the torque of motor with the series excitation:

M_em = C_e∙K∙I²_arm. (3.8)

As follows from formula (5.8) a torque of motor with the series excitation, unlike motor with the parallel excitation, is proportional to the armature current squared. Further, counting a coefficient of proportion between the excitation current and magnetic flux K = const. and, putting into the system (3.5) the values of flux Ф =КІ_arm and armature current І = √(M/C_eK), we will get equation of speed-torque characteristic of motor with the series excitation:

Ω = [U / (√M√C_e∙K)] – (R_arm + R_ew) / C_e∙K. (3.9),

where R_ew - resistance of excitation winding.

As follows from formula (3.9), speed-torque characteristic of motor with the series excitation is a hyperbolical curve, thus this curve does not cross a y-axis that is frequency of rotor rotation at the ideal idling equals to infinity.

In the real motor at idling always there is some load moment M_o on the shaft, and also exists flux of remanent magnetism. These two factors limit frequency of rotation at idling by the eventual size which, however, far exceeds the legitimate values. Therefore in the systems, where they use the motors with the series excitation, take measures which prevent work of motor in the mode of idling.

The arbitrary increase of rotation frequency of motors with the series excitation at their approaching to the mode of idling is called racing of an engine.

We will consider physical sence of racing. How already it was marked, at the ideal idling a back EMF E = C_e∙Ω∙Фequals to supply voltage U, as a result the current of armature circuit equals to zero. But in motor with the series excitation equality to the zero of armature current means equality to the zero of magnetic flux (ignore permanent magnetism). Then, in order that back EMF counterbalances network voltage, endless frequency of rotor rotation will be needed.

Speed-torgue characteristic of motor with the series excitation is shown onfig. 3.4.

As a result of saturation of magnetic circuit of motor with the series excitation in area of the large load and simultaneous action of demagnetizing reaction of armature a magnetic flux remains practically constant, therefore speed-torque characteristic in thisregion is linear, that it is shown on fig. 3.4 by Fig. 3.4

discrete line. From fig. 3.4 also it is possible to see, that the motor with the series excitation has soft mechanical characteristic.

The initial starting current of motor with the series excitation, as well as motor with the parallel excitation, far exceeds a nominal current and is evened:

I_st = U/(R_arm + R_ex) (3.10)

Torque characteristic of motor with the series excitation, as it appears from formula (3.8) is a quadratic parabola (fig. 3.5). But in area of the large load, from the higher adopted reasons, torque characteristic approaches linear, that it is shown on fig. 3.5 by discrete line.

Fig. 3.5