Contact Bounce Simulation Using Matlab - Electrical ... - IEEE Xplore

CONTACT BOUNCE SIMULATION USING MATLAB

H Nouri, N Larsen and T S Davies Faculty of Engineering University of the West of England (UWE) Frenchay Campus, Bristol BS16 lQY, UK.

9.2

ABSTRACT A computer based model for prediction of the contact bounce is developed using the MATLAB@simulation package. The model is based on the electro-magnetic system equations and mechanical dynamic properties of a real contactor. The validity of the present version of the model is examined against the measured coil current, pole piece displacement and contact bounce obtained from a commercially available contactor. The results agree well. For a closer correlation, the model requires further detailed development.

KEYWORDS - Contactor, Bounce Simulation, Modelling, MATLAB

NOMENCLA

m

= = = = = =

Coil Resistance. Coil Inductance. Induced back emf. Coil current. Voltage across the coil. Initial rest position of pole piece and contacts. = separation position of contactsand pole piece (Position where contacts are initially made) = The limit position of the pole piece (final position of the pole piece from rest). = Position of the pole piece with time. = Position of the contacts with time. = Velocity of the pole piece. = Experimentally determined coefficient. = Mass of Pole piece. = Mass of Contacts. = Spring strength of the pole piece mechanism (Measured). = Spring strength of the contacts (Measured). = Damping coefficient term. = Pole piece damping coefficient arising from friction etc. = Moving contacts damping coefficient.

1. INTRODUCTION

The laws of conservation of energy and momentum state that, when two finite bodies with initially different velocities collide, it is impossible for their interface to remain in contact and they bounce, unless some measure of dissipation of the initial kinetic energy occurs. The degree of bounce depends solely on the coefficient of restitution (e) which is the ratio of impulse during

0-7803-3968-1/97/$10.00 0 1997 IEEE.

restitution to impulse during deformation. For example, for two perfectly elastic bodies where e = 1 ,the velocity of separation is equal to the incident velocity. In such a case no energy is lost. On the other hand, where one or both bodies are made of a putty like material, where e 0, the bodies move in unison after the impact. The fundamentals of impact between two bodies with one degree of freedom are explained in any basic text on dynamics.

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The contact structure of a power switching device is more complicated. All methods of contact bounce control are to minimise the kinetic energy prior to impact or maximise the rate of dissipation. Previously we have reported [1] the reduction of the contact bounce on the basis of the above concept using electronics. Bantyukov et a1 [2] suggest the application of electronics for suppression of contact bounce. More recently a mathematical model based on restitution has been proposed [3]. However as yet, despite the advancement in computer power and computer-aided design tools, the contact bounce phenomena has not been investigated numerically. This paper considers a contact bounce simulation model using MATLAB/SIMULINK dynamic simulation tools. The power of this package lies with its capability to represent the generic model of non-linear systems.

2. SIMULATION MODEL MATLAB/SIMULINK dynamic simulation tools used in this study are capable of representing the generic model of

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non-linear systems of a typical contactor for simulation purposes. The construction of the model is based on a typical contactor from MTE which is rated at 4KW, 8.6 A contactor, with a coil voltage of 24 volts dc, as shown in figure 1.

Fig. 2. Shows detail of the components of MTE contactoi

In the case of a contactor, both L, and i will vary during the motion as the contacts close. From Faraday's law, an emf will be generated in the coil, given by:

Fig. 1. Photograph of MTE Contactor with a Linear Variable Displacement Transformer (LVDT).

In the photograph, the contactor can be seen mounted in a test rig with a Linear Variable Displacement Transformer (LVDT) attached to measure the motion of the pole piece on which the contacts are mounted. An exploded view of the contactor mechanism is shown in Figure 2. Each part of the contactor mechanism, electro-magnetic and mechanical, is modelled separately and then coupled to simulate the complete operation of a real contactor. To facilitate the application of the model to other types of contactor, each component which contributes to the performance of a typical contactor is defined and stored in a separate data file.

2.1 The Electro-Magnetic Part

A coil which is Carrying current i, sets UP flux- This flux = L,.i

is defined by:

C#J

(')

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eb = d(L,.i)/dt

or eb = L,.di/dt

+ i.dL,/dt

(2)

Since the inductance of the coil is a function of pole piece displacement, x, equation 2 can be rearranged as: eb = L,.dildt

+ i.[dL,/dx

.dxldt]

(3)

here x is the position of the contactor pole piece in time and dx/dt is the pole piece velocity. The inductance L, is a function of pole piece position, x, and current, i, due to saturation of the magnetic circuit. When the coil is initially energised, the magnetic path is dominated by the airgap but as the pole piece m o v s to the

f

1

closed position, the airgap reduces to almost zero and the iron becomes magnetically saturated. The variation of inductance, L,, in the present model is based on experimental data. Using a Least Squares fit, the following second order polynomial for L, is derived: L, = P,.$

+ P,,x + P3

The characteristics of a contactor having a coil with resistance R, and inductance of L, which carries current i at a supply voltage of Vi, is governed by the following relation: = i.R,

+ L,.di/dt + i.dL,ldx.dxldt

Thus, from xSepto xllmfor the pole piece, F,, = d'x/dt*. m,

+ dxldt.d, + k,x - k,(x - x,,J

For the moving contacts

(4)

where P, , Pz and P, are the constant coefficient of the fitted curve.

V,

and pole piece.

0 = (dzx,,,/dt2.m,

(7)

,

+ (dx,,,/dt).d, + k2.(xSep- xconJ

(8)

Figures 3 and 4 show the block diagrams of the models representing equations 6 to 8. The contact bounce is simulated with elasticity of the collision, set as a parameter of the model. Contact bounces are produced, when the position of the contacts in time meet the following conditions:

(5)

or

dildt = { [V - i.R,]

- [i.dL,/dx.dx/dt]

} /L,

-2.2 The Mechanical Parts

The mechanical parts of the contactor comprise the moving pole piece, which forms part of the magnetic circuit, with its associated return spring and three sets of moving contacts suspended from the pole piece on their own spring support. Initially, when the coil is energized there is insufficient force to move the pole piece. Current builds up exponentially since the coil inductance is fixed, ie the second term in equation 3 is zero. When sufficient current is flowing in the coil, the pole piece will start to move. The contactor operates in a way such that for the first part of travel, and until contacts are made, the mass of pole piece and contacts are joined. For the remaining distance the pole piece travels alone.

Set parametersin the workspace dis lacements xrest xsep and xlim spnng k, damping Sand masses main m l and each contactorrq m2

.

This 15 a model of a second order s stem constrained behveen rest position and limit posttlon rhe mass changes at x sep. where3 contactorsstop movlng Based on RS622-470 contactor

Fig. 3. Shows the block diagram of "Pole Dynamics" in the main model.

The mechanisms of such mass-spring damper systems may be simply described as second order differential equations containing lumped parameters. The equations of motion representing the dynamics of the mechanism between limits (limits defined as X,,,, Xsep and X,,,)and in piecewise form can be expressed as: for the pole piece and the contacts, From x,,,~to qep

Fin = d2x/dt2(m,

+ 3.m2) + dx/dt.d + k,.x

(6)

Following the making of the contacts, the pole piece continues to move under the influence of the magnetic force, whilst the contacts motion is determined by the characteristic equation shown, the only externally applied force arising from the suspension spring between contacts

Fig. 4. The block diagram of "Contacts Dynamics" in the main model.

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A comparison of the pole piece displacement with the measured values is shown in figure 7. The two results agree well. Also shown in figure 7 is the contact bounce phenomena. Although the duration of the bounce is approximately the same, the measured contact bounce has higher frequency bounce events. This could be. related to over simplification in modelling the actual contact mechanisms by considering lumped parameters.

3. RESULTS AND DISCUSSION

Figure 5 shows the complete simulation model. The required data, such as mass of the contacts, mass of the pole piece, spring constant and the force exerted on the pole piece at various positions within the air-gap, are all obtained experimentally.

polepiecepositionfor RS 622470 contactor and model

Fig. 5 . Shows the complete simulation model.

Shown in figure 6 is the profile of the measured and simulated contactor current. Initially, the current rises approximately exponentially until sufficient force is produced to accelerate the pole piece. The effect of the back emf is clearly evident as the current falls during the motion of the pole piece. When the pole piece reaches the end of its travel the current them rises to its final dc level. Initially, the agreement between the plots from experimental data and simulation is very good. As the pole piece moves to the closed position and the magnetic circuit becomes saturated, the modelling error become apparent. It should be said, however, that the simulation result is surprising good considering the simplistic approach adopted in determining the coil inductance variation.

0 023

-005

0

0 05 time s

01

01

Fig. 7. A comparison of measured and simulated pole piece displacement.

Inaccuracies in the results could also arise from parameters of the model which are subject to a large variation. This measurement is difficult to determine accurately because of friction, arising from the motion within the injection moulded case, and lack of position control of the moving pole piece as the air-gap is reduced in the laminated core.

Current dynamic for RS 622470 contactor and model

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I

4. CONCLUSION con.~acior... .

-0.05

0

0.05

0.1

. .. . ..

.... .

The work presented here is simplified, but nevertheless predicts characteristic behaviour of a real contactor, namely contact bounce. Results from contact bounce simulation suggest that the lumped parameter modelling of the moving contact mechanism needs to be developed further to allow a higher order description of the contact and its supporting structure. In addition, the effects of magnetic saturation in the iron parts of the contactor must be modelled more precisely. It is interesting to note that, despite these deficiencies, plots of measured and simulated current and displacement are in general agreement.

0.15

time s

Fig.

As a part of the continuing programme of work, the development of an adequate general model is likely to rank high by engineers.

The Profile ofthe measured and simulated contactor coil current.

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REFERENCES

1. T. S. Davies, H. Nouri and F. Britton,"Towards the Control of Contact Bounce," IEEE Transactionson CPMT, Vol. 19, No. 3, Sept 1995, pp 353-359.

2. E. N. Bantyukov and V. G. Ershov,"Suppressor of Contact Bounce Pulses," J. of Inst. and Experimental Techniques, Vol. 34, No. 3, Pt. 2, May-June 1991, pp 709-709. 3. J. W. McBride and S. M. Sharkh,"Electrical Contact Phenomena During Impact," IEEE Transactions on CPMT, Vol. 15, No. 2, Apr 1992, pp 184-192.

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