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Starting of DC motor with independent excitation to the main speed at one stage of starting rheostat
Transient process of DCM IE starting to the main angular speed occurs in case of motor energizing from DC network at connecting the linear contactor КМ into armature circuit, see figure 5.1.
Figure 5.1 – Scheme of starting with switched on starting rheostat for all starting period.
In considered scheme for all starting period a resistor
Let’s assume that executional mechanism, for which DCM IE operates, will be of 1-st class, so
For simplification let’s consider that only electromechanical transient process occurs (electromagnetic transient process is neglected), so armature inductance is absent
Let’s consider that power source of armature circuit has significant power, so
Also let’s consider that DCM IE is compensated (the armature reaction is eliminated), then magnetic flux during the starting doesn’t change, i.e.
Taking into account these simplified assumptions the equilibrium equation at starting will have view: - the equation of voltage equilibrium
- the equation o motion
In equations (5.1) and (5.2) their components have such values. Armature e.m.f.:
where Dynamic moment:
where
Moment of motor:
Taking into account these markings, from the equation (5.2) let’s define the value of armature current and substitute into equation (5.1)
Let’s divide the last equation on
Let’s introduce such markings
Figure 5.2 – Starting static characteristic.
In its turn electromechanical time constant
i.e.
It is easy to prove:
because because
Ratios (5.6), obtained from the consideration of physical essence of initial starting moment, affirm written equation (5.5). From the expression (5.5) a physical essence of electromechanical time constant can be formulated: Electromechanical time constant is time, during which ED, that have inertia moment From (5.5) it is running out, that value Taking into account (5.3), (5.4) and accepted markings, equations (5.1) and (5.2) can be represented in form
where Solution of equations (5.7) and (5.8) relatively to Theoretically a starting process ends in infinitely long time, but in practice it can be considered, that starting process ends at
because angular speed in this case differs from its steady state value not more than on (5 – 2)%. In such a way, from time
а – exponents of armature current damping; b – exponents of angular speed increasing. Figure 5.3 – Graphs of current and speed changing at starting.
Though starting would be realized all time under the action of moment In first case there was idling rate, in second – operation under the load – There are analogical considerations also defining the electromechanical constant
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