THE 8th INTERNATIONAL SYMPOSIUM ON ADVANCED TOPICS IN ELECTRICAL ENGINEERING May 23-25, 2013

Bucharest, Romania

3D Finite Element Analysis of a Miniature Circuit Breaker

Dumitru Pop, Liviu Neamt, Radu Tirnovan, Dorin Sabou

Technical University of Cluj-Napoca dan.pop@enm.utcluj.ro, liviu_neamt@ubm.ro, radu.tirnovan@enm.utcluj.ro, dorinsabou@yahoo.com

Abstract- In this paper a miniature circuit breaker (MCB) is analyzed using a finite method analysis (FEA) software. Once the 3D model was implemented, a series of simulations were carried out in order to find out the forces that appear inside the electromechanical trip unit and what influences the plunger to trip faster. Also, the influence of the material nonlinearity is emphasized in order to understand the real behavior of the material in a specific applied magnetic field.

Keywords: circuit breakers, short circuit currents, finite element methods, electromagnetic forces, magnetostatic

I. INTRODUCTION

Low voltage miniature circuit breakers (MCB) are electromechanical devices used to protect people and electrical equipments against a short circuit and overload. They are used in residential, commercial and industrial applications. An MCB is a better alternative to a fuse since it does not require replacement once an overload is detected and it can be easily reset offering improved operational safety and greater convenience [1]-[4]. A section showing the principal parts of a miniature circuit breaker is presented in Fig. 1.

Miniature circuit breaker construction is simple, yet very precise. In fact, a miniature circuit breaker has no replacement parts. It is not designed to be maintained. When a unit goes bad, it is simply replaced.

Low voltage miniature circuit breakers use an electromechanical trip unit which is integrally mounted into the circuit breaker and is temperature sensitive. Thermal magnetic trip units act to protect the conductors, safeguarding equipment under high ambient conditions and permitting higher safe loading under low ambient conditions. This trip unit utilizes bimetals and electromagnets to provide overload and short circuit protection. The thermal trip portion is used for overload protection. Its action is achieved using a bimetal heated by the load current. On a sustained overload, the bimetal will deflect, causing the operating mechanism to trip. The magnetic trip portion is used for short circuit (instantaneous) protection. Its action is achieved with an electromagnet whose winding is in series with the load current. When a short circuit occurs, the current passing through the conductor causes the electromagnet’s magnetic field to rapidly increase, attracting the armature and causing the circuit breaker to trip [5].

II. FINITE ELEMENT METHOD

The finite element method (FEM) is a numerical technique that was originally introduced as a method for solving structural mechanical problems. The finite element method has emerged as a universal method for the solution of differential equations. Much of the success of the finite element method can be contributed to its generality and simplicity, allowing a wide range of differential equations from all areas of science to be analyzed and solved within a common framework. [6] FEM solves a complex problem by redefining it as the summation of the solution by a series of interrelated simpler problems. The first step is to subdivide (i.e. discretize) the complex geometry into a suitable set of smaller ‘elements’ of ‘finite’ dimensions when combined from the ‘mesh’ model of the investigated structures. Each element can adapt a specific geometric shape (i.e., triangle, square, tetrahedron, etc.) with a specific internal strain function. Using these functions and the actual geometry of the element, the equilibrium equations between the external forces acting on the element and the displacements occurring on its nodes can be determined [7].

The analysis of a electromagnetic problem can be made by solving Maxwell’s equations system: ∇ ⋅D = ρ , (1)

Fig. 1. Principal parts of a miniature circuit breaker

a – upper terminal; b – arc chamber; c – fixed contact; d – lower terminal; e- moving contact; f – electro-magnetic protection.

978-1-4673-5980-1/13/$31.00 ©2013 IEEE

∇ × E = −

∂B∂t

, (2)

∇ × H = J +

∂D∂t

, (3)

∇ ⋅ B = 0, (4) where: E – electric field [V/m] B – magnetic induction [T] D – electric induction [C/m2] H – magnetic field [A/m] J - current density [A/m2] ρ – charge density [C/m3].

Today, the FEM technique is considered to be one of the best alternative methods for solving a wide variety of practical problems efficiently.

III. SIMULATION OF A MCB

A miniature circuit breaker was implemented in Infolytica MagNet, respecting the size, shape and place of every component in a real MCB (Fig. 2). Once the 3D model was created, a number of magnetic FEA simulations were carried out in order to find answers to different problems. In this paper we present the results obtained in magnetostatic simulations where we analyzed the forces produced by the electromechanical trip unit in different situations (Fig. 3).

Magnetostatic problems are problems in which the fields are time-invariant. In this case, the field intensity (H) and flux density (B) must obey:

∇ × H = J , (5) ∇ ⋅ B = 0, (6) subject to a constitutive relationship between B and H for

each material: B = μH , (7)

If a material is nonlinear (e.g. saturating iron), the permeability μ is actually a function of B:

μ =

BH (B)

. (8)

Flux density is written in terms of the vector potential, A, as: B = ∇ × A , (9) then (5) can be rewritten as [8]:

∇ ×

1μ(B)

∇ × A

= J . (10)

The associated functional of the equation (9) is:

F( A) =12

1μ r

(∇ × A)V ⋅ (∇ × A)dV −

−μr J ⋅ AdVV

.

(11)

In Fig. 3 the tripping mechanism of the MCB simulated is presented. The heart of the mechanism is the solenoid which works on the principle of electro mechanism. The coil of the solenoid is designed in such a way that when current passing through it is within the permissible value, the magnetic force produced is not enough to pull the plunger. When the current exceeds the permissible value, the magnetic force also increases and this magnetic force push the plunger inside towards the center of the coil. When the plunger moves it also pushes the moveable contact and forces it to separate from the fixed contact thereby tripping the circuit. The plunger is connected to a spring from inside the electromagnetic coil and as the plunger moves towards the center of the coil, the spring gets loaded. After the MCB trips (i.e., the moveable contact separates from the fixed contact and the current stops flowing) the spring forces the plunger back to its normal state without disturbing the moveable contact [9].

In our simulations we analyzed these situations: the solenoid has/has not a steel shield and the material

Fig. 2. The 3D model of the miniature circuit breaker.

Fig. 3. The electromechanical trip unit modeled in 3D FEA.

(Steel1010) is considered linear or nonlinear. The shield serves like an armature for the electromechanical trip. The ferromagnetic material Steel1010 have a constant relative magnetic permeability (linear consideration of material) μr=902.6 and the B-H curve as illustrated in Fig. 4.

Fig. 4. B-H curve of Steel1010.

The results obtained at different current values, considering the linearity of the material, are presented in Table I. Bolded cells represent the most important component of the forces for the trigger mechanism. In Fig. 5 we represent the y component of the force over the plunger.

TABLE I RESULTS OBTAINED IN SIMULATIONS CONSIDERING THE MATERIAL LINEAR

F [N] with shield

Current [A] Fx Fy Fz Ftotal

16 -1.46E-03 -2.84E-02 4.33E-04 2.84E-02

160 -0.14383 -2.84E+00 0.025238 2.8423

1600 -14.571 -283.65 4.3316 284.06

4800 -131.14 -2552.9 38.984 2556.5

F [N] without shield

Current [A] Fx Fy Fz Ftotal

16 7.32E-04 -1.05E-02 6.96E-04 1.05E-02

160 0.071674 -1.05E+00 0.070899 1.0531

1600 7.3151 -104.73 6.9558 105.21

4800 65.836 -942.54 62.602 946.9

Considering the nonlinearity of the material are presented

in Table II. In Fig. 6 we represent the y component of the force over the plunger. It can be observed the big difference, in terms of forces over the plunger, between these two

simulations data. This represents the real behavior of the plunger, that’s why it’s very important to take into account the nonlinearity of the material [10].

Fig5. The y component of the force over the plunger considering the material linear.

TABLE II

RESULTS OBTAINED IN SIMULATIONS CONSIDERING THE NONLINIARITY OF THE MATERIAL

The error between these two values (considering the

material linear or nonlinear) for both situations (with or without shield) is given by the expression:

e[%] =

Flinear − FnonlinearFlinear

⋅100, (12)

and it’s represented in Fig. 7.

F [N] with shield

Current [A] Fx Fy Fz Ftotal

16 -1.36E-03 -2.68E-02 3.67E-04 2.68E-02

160 -0.12234 -2.51E+00 0.037522 2.5095

1600 0.26014 -30.091 2.1333 30.168

4800 5.1589 -79.874 5.8968 80.257

F [N] without shield

Current [A] Fx Fy Fz Ftotal

16 7.43E-04 -1.03E-02 6.75E-04 1.04E-02

160 0.06907 -1.07E+00 0.047461 1.0782

1600 1.8974 -25.579 1.3894 25.687

4800 6.4605 -73.488 4.6109 73.915

Fig. 6. The y component of the force over the plunger considering the

material nonlinear.

Fig. 7. The error between the two cases analyzed.

IV. CONCLUSIONS

Finite element method is one of the most used methods for numerical analysis of electromagnetic fields. One of the main advantages of this method is that once a model is implemented, it can be used for the solution of any problem simply by changing parameters. In this paper, a 3D model of an MCB was realized and a magnetic finite element analysis

of the electromechanical trip unit was done in order to find out the force values that appear inside at different current values. This is important to the manufacturers because the trigger must act only when a fault occurs and knowing the forces that appear inside the trigger unit gives a better insight

We also emphasized the importance of the material nonlinearity because designers must consider the real behavior of the materials in applied field, being known that the linearity of materials leads to unsatisfactory results.

ACKNOWLEDGMENT

This paper was supported by the project "Improvement of the doctoral studies quality in engineering science for development of the knowledge based society-QDOC” contract no. POSDRU/107/1.5/S/78534, project co-funded by the European Social Fund through the Sectorial Operational Program Human Resources 2007-2013.

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