Electromechanical Modeling Of A Contactor With AC Coil

Abstract

Two ways of modeling a contactor with AC coil are shown. Both models are based on the explicit definition of the

inductances by lumped parameters, and the difference between them is the considering or not of the effect of the

shading rings. The equations were formulated to obtain the contact operation time and to describe the contactor coil

current, when the coil is fed with different values of the AC source voltage. The comparison between theoretical and

experimental results shows that the models are satisfactory in both cases. This demonstrates the possibility of obtaining

accuracy without considering the shading rings. The main advantage of the inclusion of the effect of the shading rings is

the obtaining of a qualitative description for the currents in the shaded rings.

1. Introduction

The basic electromechanical equations for the description of the transient behavior of the contactors with DC coil can

be found in some textbooks [1-5]. However, some simulation details for the contactors are only described in specialized

literature, for example: a) the non-linear effect due to the limits for the armature displacement [6-7], b) the

discontinuities in the armature path, due to the changes in the springs and masses in motion [8-9], c) the effects of the

small air gaps between armature and core when the contactor is closed [9].

The contactors with AC coil usually have shading rings in a part of the core. The objective of the shading rings is to

obtain a phase-shift between two magnetic fluxes in the armature, in order to always achieve an instantaneous net force

greater than zero on the armature because this avoids the mechanical vibrations that would be produced without these

shading rings. Different articles show diverse details about the simulation of contactors with AC coil and shading rings [8-17], by using the finite element method [8-13] or without using it [14-17].

On the other hand, the application of correction factors for the equivalent lengths and the equivalent areas of the

magnetic field paths is usual in the analysis of the magnetic circuits of transformers [18-19] and inductors [20-21].

Although the application of similar factors is not usual for contactors, there are examples of their use for contactors with

AC coil [14-16]. Such correction factors were not included in this article because the results of the models were

sufficiently accurate without the need of using them.

2. Basic simplifications

The following simplifications were used for the model:

a) Only an equivalent spring was considered, whose force varies linearly with the armature movement.

b) The contactors usually have different springs, related to the armature and the auxiliary contacts. The effect of such

different springs was not considered.

c) The effect of the small collisions, produced in the core during the armature travel, was not considered.

d) Changes in the masses in motion, which could occur during the armature travel, were not considered.

e) An equivalent mass was considered, that relates the accelerating force with the armature acceleration.

f) Only a linear variation of the friction force with respect to the armature velocity was considered.

g) The nonlinear characteristic of the ferromagnetic core of the contactor was not considered.

h) The presence of the iron remnant flux at the energizing instant was not considered.

i) Correction factors for equivalent length and/or equivalent area of the magnetic paths were not considered.

j) Effect of losses in the ferromagnetic core (by hysteresis and/or by eddy currents) was not considered.

The first approximation indicates that the ratios between the iron equivalent areas and the gap equivalent areas were

assumed to be the same for the correspondent paths of the three magnetic fluxes (φ, φ

1 and φ

2). The second approximation

indicates that the conductor area of the shading rings is insignificant, in comparison with the iron equivalent areas. The

third approximation indicates that the equivalent lengths are assumed to be the same for the paths of φ

1 and φ

2 in the iron

regions.

3.3. Number of independent parameters for each model

The model without the effect of the shading rings is in function of 8 parameters (x0, C1, C2, d, K, m, BF, R), and the

inductance is defined by only three of them.

The model with the effect of the shading rings has 12 parameters (N, a, K1, K2, [K3/K4], d, K, m, BF, x0, R, Req), the

inductances are in function of 6 parameters, and this model has one parameter (Req) for the electric circuit of the shading

rings, where direct measurements are not possible.

4. Results

4.1. Comparison with experimental measurements

A contactor with a 230VAC coil was tested. The source rms voltage value (VRMS) for the tests was varied in 11 steps

between 135V and 230V. The source voltage is expressed as:

V=√2 VRMS Sin (ω t + θ) (50)

ω: Angular electric frequency.

θ: Angle at the energizing instant.

For each voltage magnitude, the contactor was energized for values of θ near to 0° and near to 90°. The graphic

results show the measured current (α), and the current obtained from simulation (β); the measured value of θ is

indicated for each case. For the sake of simplicity, only the graphs for 6 voltage magnitudes are shown in this article.

The parameters for the models were found by a trial-and-error procedure. Only the gap length and the coil resistance

were assumed as known parameters (d=0.006m, R=500). There were attempts for using an optimization tool for

minimizing the error of the approximation; however, these attempts were not successful.

Fig. 2 and Fig. 3 show the experimental measurements and the results for the model that does not consider the effect

of shading rings. Fig. 4 and Fig. 5 show the corresponding results for the model that considers the effect of shading

rings. Table 1 and Table 2 show the value of the parameters for the models, expressed in the International System of

Units (SI).

Closing of the normally open contacts is produced before the end

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