OPTIMUM DESIGN OF A NOVEL SOLENOID USING ANSYS/EMAG

W. Wu, H.C. Lovatt

Telecommunications & Industrial Physics CSIRO

Sydney, NSW, Australia

P.A. Watterson

Faculty of Engineering UTS

Sydney, NSW, Australia

ABSTRACT

The design of a new type of cylindrical DC solenoid is presented in this paper. The solenoid comprises two parts, a stator and a moving plunger. The plunger compresses a spring with a minimum force of 7.1 N over an 8 mm travel. ANSYS was employed for the design and optimization, incorporating the non-linear characteristic of the magnetic material. This paper gives an overview of the modelling and optimization procedure involved in the analysis.

INTRODUCTION

Solenoids are electromagnetic devices that provide linear motion over a short displacement. Due to their simplicity, reliability, and low cost, solenoids are widely used in switches, relays, and valves. The force-displacement characteristic of a solenoid is of primary importance. Therefore, the ability to predict the force characteristic over the displacement range and to optimize the physical dimensions of the solenoid is crucial. Cut-and-try methods and lumped reluctance calculations [1] have been used but these suffer from errors. With the development of various numerical techniques, finite element modelling can be employed for the analysis and design of solenoids [2].

This paper presents a new type of cylindrical DC solenoid, with a notch in the perimeter of the solenoid, as shown in Fig. 1, to produce a flatter force-displacement profile. The stator is hollowed out to allow a large coil with low copper loss. The plunger is attached to a compression coil spring that pushes the plunger to the top position. When a DC current is applied in the stator coil, an attractive force between the plunger and stator is generated which compresses the spring and pulls the plunger to the bottom position. The notch in the plunger gives the solenoid the appearance of a linear version of a switched reluctance motor.

ANSYS was employed for the analysis and design optimization, incorporating the non-linear characteristic of the magnetic material. The practical modelling considerations and optimization procedure are described in this paper. The notch in the plunger is shown to improve the force-displacement characteristic.

(a) Notch-less plunger

(b) Notched plunger

Stator ironCoil

Spring

Plunger

Spring

Stator ironCoil

Plunger

Fig. 1 Layout of the cylindrical DC solenoid

Design optimization is achieved by using the parametric design language in ANSYS and defining five variables representing the main dimensions. The forces produced by the

solenoid for two different air gaps at two critical positions are represented by four state variables. The material cost is defined as the objective function. Numerous iterations are performed automatically by ANSYS wherein the five main dimensions are varied so as to minimize the objective function, namely material cost, while meeting the force requirement.

Different options available in ANSYS for calculating the force were compared. ANSYS offers two search methods to find the optimum solution: a sub-problem approximation method and a first order method. The optimization is compared using these two methods individually and using a combination of the two methods.

FINITE ELEMENT MODELLING

As the solenoid is axisymmetric, a 2D axisymmetric static analysis is employed. In order to calculate the force over a range of displacement, a parametric model is defined with the displacement of the plunger as an argument. The stator iron and the plunger are represented by their non-linear B-H characteristic. The coil is modelled as air. The meshes for the stator and the plunger are created separately. Half of the stator with its surrounding air is meshed and mirrored to form the whole stator. The mirror image approach is also applied to the plunger and the air gap meshes. Such mirror symmetric meshes are expected to result in lower numerical error. The plunger and air gap meshes are then moved by the specified displacement and joined to the stator mesh along the inner side of the stator by using the CEINTF command. There is no need to re-mesh the stator and the plunger region whenever the plunger moves, which saves computation time. Air around the solenoid is modelled to a distance from the solenoid of approximately 10 times the air gap axially and 3 times radially. Fig. 2 shows the meshes with iron, coil, and air, boundary conditions, and Virtual Work displacement, when the plunger is at the bottom and the top positions.

ANSYS offers two methods to calculate the magnetic force: Maxwell stress and Virtual Work. It has been found that the Virtual Work method is less dependent on mesh size and shape than the Maxwell stress method. The Virtual Work displacement is defined for the nodes in the plunger.

The force of the solenoid depends on the displacement of the plunger. Zero displacement is defined when the bottom surface of the plunger is aligned with the bottom of the stator. Fig. 3 shows the effect of the plunger shape on the force-displacement profile of the two solenoid designs (see Fig. 1). The notch-less solenoid gives a higher peak force whilst the solenoid with a notched plunger gives a more uniform force-displacement characteristic. Therefore the notched solenoid is a better choice for long-travel applications.

DESIGN OPTIMIZATION

Based on the above modelling, a design optimization for a solenoid was performed with the objective function being

minimum cost. The solenoid is constrained to pull a minimum force of 7.1 N against a spring over an 8 mm travel. The solenoid is required to work for the air gap in the range of 0.4±0.2 mm, to allow for manufacturing tolerances.

The notched plunger as shown in Fig. 1 (b) was used due to its better force-displacement profile. From Fig. 3 it can be seen that the force is zero at zero displacement and does not reach the required force until the plunger has moved some distance from the bottom of the stator.

1

(a) Meshes at the bottom position showing materials,

boundary conditions, and constraint equations

ANSYS 5.4 JAN 23 199810:36:04 PLOT NO. 1ELEMENTSVIRTUAL DISPL.VTMN=0 VTMX=1

1

A CE NFORRFOR

ZV =1 DIST=.03861 XF =.0423 Z-BUFFER 0 .111111 .222222 .333333 .444444 .555556 .666667 .777778 .888889 1

(b) Meshes at the top position showing Virtual Work

displacement

Fig. 2 Finite element meshes

0 1 2 3 4 5 6 7 8 9 10 11 120

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Notch-less plunger Notched plunger

Forc

e (N

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Plunger displacement (mm)

Fig. 3 Effect of different plunger shapes

Fig. 4 Design variables of the solenoid

The downward solenoid forces of the plunger at the top and the bottom of its travel were used as constraint variables, and set to be greater than 7.8 N. The margin of 10% higher than the maximum required force of 7.1 N was added to allow for errors in the finite element calculation. The forces at the top and bottom of the travel were calculated at the extremes of the air gap length, 0.2 and 0.6 mm, giving a total of four constraint variables for the forces. In addition, the consumed power at the minimum operating temperature and the winding temperature at the maximum operating temperature were also set as constraint variables.

It was found that the calculation of solenoid forces was sensitive to magnetic saturation in the plunger. Therefore a non-linear analysis had to be used for the optimization,

As shown in Fig. 4, five dimensions were defined as design variables: the radius to the centre of the air gap (rx), the radial thickness of the stator (st), the radial thickness of the plunger (pt), the stator and plunger tooth height (z1), and the plunger notch height (z2). All other dimensions were fixed.

ANSYS offers two optimization methods: the sub-problem approximation method and the first order method. Although the first order method is much more robust and accurate than the sub-problem approximation method, it is computationally intensive. To provide a rapid search for the optimum design, a combination of these two methods was adopted. The sub-problem approximation analysis was initially performed to locate an approximate optimum in the feasible design space, and then the first order method was used to perform the final search.

For design optimization it is necessary to provide an initial guess for the design variables. The closer the guess is to the final design the quicker the optimization search. To speed up the optimization it is has been found useful to split the procedure into stages. It is also helpful to initially use a linear analysis, since this is considerably quicker than a non-linear analysis. The two stages used for the design optimization were:

1. Linear analysis for the case of maximum air gap, 0.6 mm, calculating the force at the top of the travel only, using the sub-problem approximation method;

2. Non-linear analysis at both the extreme air gaps, 0.2 and 0.6 mm, calculating the forces at both the top and bottom of the travel, using the sub-problem approximation method first and then the first order method.

Through consideration of the optimization results and the available wire gauge sizes, a practical design was finalised. The force against travel position for different airgap lengths has been determined and is shown in Fig. 5. Fig. 6 shows the magnetic flux line and flux density distribution when the plunger is at the bottom and top of the travel.

0 1 2 3 4 5 6 7 8 9 10 11 120

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Airgap = 0.2 mm Airgap = 0.4 mm Airgap = 0.6 mm

Forc

e (N

)

Plunger displacement (mm)

Fig. 5 Force-displacement profiles for different airgap lengths

ANSYS 5.4 JAN 23 199811:12:32 PLOT NO. 1ELEMENT SOLUTIONSTEP=2 SUB =1 TIME=2 BSUM (NOAVG)RSYS=0PowerGraphicsEFACET=1SMN =.111E-05 SMX =2.187

1

.111E-05 .242965 .485929 .728893 .971857 1.215 1.458 1.701 1.944 2.187

NODAL SOLUTIONSTEP=2 SUB =1 TIME=2 R*AZ RSYS=0SMX =.107E-03

1

A =.592E-05 B =.178E-04 C =.296E-04 D =.414E-04 E =.533E-04 F =.651E-04 G =.770E-04 H =.888E-04 I =.101E-03

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(a) At the bottom position

ANSYS 5.4 JAN 23 199811:19:26 PLOT NO. 1ELEMENT SOLUTIONSTEP=2 SUB =1 TIME=2 BSUM (NOAVG)RSYS=0PowerGraphicsEFACET=1SMN =.216E-06 SMX =3.307

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.216E-06 .1 .2 .3 .4 1.5 2 2.5 3

NODAL SOLUTIONSTEP=2 SUB =1 TIME=2 R*AZ RSYS=0SMN =-.169E-04 SMX =.264E-04

1

A =-.157E-04 B =-.133E-04 D =-.846E-05 E =-.605E-05 G =-.124E-05 H =.117E-05 J =.598E-05 K =.839E-05 M =.132E-04 N =.156E-04 P =.204E-04 R =.252E-04

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(b) At the top position

Fig. 6 Magnetic flux line and flux density of the solenoid

CONCLUSION

A new type of cylindrical DC solenoid that gives a flatter force-displacement characteristic than traditional designs has been presented. ANSYS has been employed to model the performance and to find the optimum dimensions for the solenoid taken into account the manufacturing tolerance of the air gaps. ANSYS has proven to be an effective and efficient tool for analyzing and optimizing the design of this novel solenoid.

REFERENCE

[1] Fitzgerald, A.E., Kingsley, C., and Umans, S.D., 1992, “Electric machinery,” 5th Edition, McGraw-Hill Kogakusha Ltd.

[2] Bax, A., Anderson, C. Yaksh, Ostergaard, D., 1994, “Finite element analysis of an AC solenoid including the effects of harmonic loading and magnetic saturation,” Proceedings of ANSYS Conference and Exhibition, Pittsburgh, USA, May 2-6, pp 9.31-9.44