Many novel applications using giant magnetostrictive actuators (GMA) require their actuators output bidirectional strokes to be large enough to drive the load. In these cases, the sophisticated method to form such a sufficient bias field with minimum power and bulk consumption should be considered in the principal stage of GMA design. This paper concerns the methodology of bias field design for a specific GMA with stack PMs and GMMs (SGMA): both loop and field models for its bias field are established; the optimization method for given SGMA structure is outlined; a prototype is fabricated to verify the theory. Simulation and test results indicate that the bias field could be exerted more easily using SGMA structure; the modeling and optimization methodology for SGMA is valid in practical design.

In the development of novel hydraulic servo valve (EHSV) serving in aerospace industry, giant magnetostrictive actuator (GMA) is a thriving device to generate micro stage displacement fast and precisely [

Each method has its own advantages and disadvantages. Method (a) is easier to be realized and the field intensity is more readily to be adjusted using this method, but it consumes more power and therefore increases the total power losses. Furthermore, two coils within in GMA will induce mutual inductance reducing the driving efficiency and enlarge the total radius dimension considerably. For instance, Joshi and Kadoli developed a DC biased GMA with two concentric coils; inductance for both coils with GMM core is, respectively, 16.45 mH and 18.3 mH, the flux leakage of outer coil reaches 12%, and overall radius of outer coil is 4.1 times that of GMM rod [

The traditional configuration for PM bias in GMA is based on “tube-like” magnets. With a GMM rod located in the innermost of the PM tube, this configuration helps to form a uniformed longitudinal field all through GMM bar [

Another configuration employed distributed PMs to provide bias field; PM patches are usually located on poles of GMM bar. This configuration helps to relieve the end effects of long GMM rod; the disk shape PMs are placed in line with GMM rod which saves a lot of transversal dimension and therefore being more easily to be located within a mechanical amplifier. Braghin et al. developed a low frequency magnetostrictive inertial actuator for vibration control with this configuration, which reduces the eigenfrequency of actuator and extends its stroke; this configuration also helps to reduce the general size of actuator thus allowing to mount it even in narrow cavities [

Despite the potential of distributed PMs in GMA design, the most crucial problem of this arrangement is that the field intensity will not be uniformed along the rod, especially when the aspect ratio for GMM is large. How to gain an acceptable homogeneous bias field in long GMM rod with little bulk penalty has become a hot point for recent researchers. Zhang et al. developed a triple-ring PM structure, in their design; three PM rings are located surrounding both ends and the center of GMM rod; in this way the field homogeneity was greatly improved for GMM rod with an aspect ratio larger than 3.5 [

Our institute focuses on the development of novel electrohydraulic servo valves served in aeronautic applications, which require the actuator to output a large bidirectional stroke precisely. According to the above analysis, the bias field implementation for this specific case is a little troublesome for traditional PM layout: a tube-like magnet will make it bulky and magnet pairs on both ends cannot ensure a uniformed field distribution. In this paper, we employ a configuration which geometrically iterates the poles PM case; that is, pole magnets are located in series and alternatively with short GMM patches; in this way the aspect ratio for each GMM patch is not so large and the transversal dimension could be saved; this structure is named as stack GMA (SGMA) because of its specific structure [

3D model of pole GMA and stack GMA.

Pole GMA

Stack GMA

Generally, there are mainly two different analysis methods for magnetic field in ferromagnetic materials, namely, loop method and field method. Loop analysis is conducted based on the assumption that field distribution is homogeneous in radius span; therefore, the GMM rod could be modeled in its longitudinal direction as a network of magnetic circuits [

Field method denotes a more precise analysis using FEM package. The analysis is based on Maxwell equation; the field distribution is calculated by resolving partial differential equations simultaneously on each node. It provides a continuous description on field distribution but consumes more computing resource. This method also fails to get an overall parametrical solution, let alone parametrical optimization and identification. Therefore, this method is more attractive if we are only interested in field analysis of a certain structure [

In this paper, we focus on the specific layout of SGMA; both loop and field models for its particular bias field are built. Considering the unevenness of axial direction, more magnetic circuits are employed. A general model for bias field in SGMA is built. This model is compatible with arbitrary GMM number and arbitrary number of divided loops in each GMM bar. Therefore, it provides guidance for SGMA design. In field analysis, a more precise field distribution is studied using FEM for different design parameters. The study results of field analysis are proved to be supportive and compensable for loop analysis. A specific superposition effect of multiple PMs is observed. Dealing with this superposition effect, an optimization for SGMA structure is conducted. This paper provides basic analysis for SGMA which could be used as a premier guide for its design; the loop model can be coupled easily with magnetization and magnetostriction procedures in order to study its overall dynamics.

The structure of this work is outlined as follows: Section

The single GMM structure includes a long GMM bar with PM patches attached on its both ends. This structure stands for the basic element of a SGMA, since the multi-GMM case could be regarded as a structure iteration of this basic structure. Unlike the traditional configuration, GMM bar is located within the center of a tube-like PM or DC current coil; in SGMA, GMM bar is embedded between a pair of PM patches [

The loop analysis is based on the magnetic circuit theory. As it is stated above the unevenness of bias field makes it necessary to divide the rod into several segments. In most of the previous works [

3D diagram for an element and its equivalent magnetic circuit.

In Figure

The expression of magnetic reluctance in each section is defined as

In the above equation,

Practical test curves of GMM magnetization.

In previous works [

In mesh current analysis, the state variables are selected as the fluxes flowing within each mesh loop

The above equation could be transformed into a matrix form:

Submitted with the corresponding parameters, an explicit expression of

Some qualitative conclusion could be achieved from (

Although a 3-loop model could describe the alteration pattern of bias field within GMM bar, this description is rather rough. In order to provide a more explicit loop analysis, this paper extends this method to build a multiloop model for bias field alteration.

Consider the mesh flux equation (

This extended model provides a more explicit description of the variation pattern of field distribution along axis position of GMM bar, especially when the aspect ratio is larger.

The governing equation of static field within GMM bar could be expressed as

In the above equation,

In the above equation,

The field distribution, represented by both color table and contour lines, in single GMM case is detailed in Figure

Contour plot of magnetic field distribution in single GMM case.

According to Figure

Semimajor and semiminor axis.

The comparison of magnetic field distribution, modeled by FEM as well as different loop analysis, is exhibited in Figure

Axial field distribution described by multiloop model and FEM analysis.

According to Figure

Percentage difference of magnetic field along axial and radius position of GMM with different design parameters.

Aspect ratio | Difference in axial magnetic field | Difference in radius magnetic field |
---|---|---|

1 | 5.03% | 0.27% |

2 | 11.91% | 0.17% |

4 | 28.91% | 0.12% |

| ||

Remanent flux density | Difference in axial magnetic field | Difference in radius magnetic field |

| ||

1.2 T | 15.95% | 0.08% |

1.4 T | 28.91% | 0.12% |

1.6 T | 37.64% | 0.18% |

Table

When the axial dimension is much larger, multi-GMM structure will be employed in SGMA design, since this structure helps to enhance the field homogeneity along GMM bar. According to the analysis in former sections, multi-GMM structure could be regarded as a structural iteration of the basic single GMM structure. Therefore, the analysis method in single GMM case could be extended to multi-GMM structure.

A multi-GMM case of SGMA structure could be regarded as a structural iteration of single GMM case; a diagram for its overall magnetic circuit is simplified in Figure

Overall magnetic circuit model for the linear-arrayed GMA.

Based on the mesh circuit method detailed in Section

In the above equation,

Figure

Average magnetic field strength variation when different GMM numbers and different loop numbers are employed.

According to Figure

The setup for field analysis is similar to single GMM case, except for a geometrical iteration for GMM patches; a flow chart for this geometrical iteration method in a FEM platform is exhibited as Figure

Flow chart for geometrical iteration of multi-GMM structure.

Based on the multi-GMM case loop model (

Magnetic field contour in GMM domain and axial distribution comparison with loop model.

According to Figure

A field analysis allows us to study more explicitly the unevenness of field distribution within GMM patches. The unevenness of axial magnetic field in GMM rod is evaluated via the following factor [

Figure

Average magnetic field and uneven distribution coefficient in different GMM bar number.

Figure

Supported by loop and field analysis, the proposed structure proves to adjust to the situation better when a larger bidirectional stroke is required: in that case, the total length of GMM bar has to be very long; a traditional structure with tube-like PM will make the overall structure very bulky; the structure with two PMs on the end of single GMM bar will make the axial field poorly distributed ascribed to its large aspect ratio.

In spite of the merits in this multi-GMM structure, there are some practical issues to be considered: when employing more PMs, the total length of this GMM-PM array has to be extended, which means more turns of coil and more energy consumption; too many patches of GMM will make it difficult to fabricate; the interfaces between alternate PMs and GMMs are more vulnerable to crack after considerable duty circles and therefore degrade the mechanical strength as well as the reliability of overall structure. Therefore, an appropriate GMM number should be selected according to the required bias field, or fundamentally the expected stroke and power consumption. Figure

Design stages for the basic structure of SGMA.

According to the field analysis result for multi-GMM case, the superposition effect deteriorates the axial field distribution in GMM; in this section, an optimization method is proposed to ameliorate these effects.

Indicated by field analysis results, there are three parameters that could be tailored in optimization. According to Table

The objective function for this optimization process is selected as the unevenness function detailed as (

Based on observation of the curves in Figure

The alternative characteristics indicate that the average field intensity near the mid-perpendicular tends to be weaker. In this case, in order to obtain a uniform distribution, length of GMMs near the center is supposed to be shorter and therefore sets a lower boundary for parametrical optimization:

With the objective function detailed as (

Axial field distribution before and after optimization.

Table

Optimization result of each PM length in different cases.

| | | | | | |
---|---|---|---|---|---|---|

Initial unevenness factor | 3.03% | 2.24% | 1.77% | 1.45% | 1.21% | 1.15% |

Optimized unevenness factor | 2.98% | 2.18% | 1.72% | 1.42% | 1.19% | 1.06% |

According to the above analysis, a general roadmap in optimal design of linear-arrayed GMA could be summarized as the following steps: to begin with, the number of GMM patches in given condition should be determined following the design procedure detailed in Figure

Both magnetic field and displacement tests are conducted; the test system is exhibited in Figure

Setup for SGMA test system.

The magnetic field intensity tests and displacement tests are conducted, respectively, using Tesla meter and eddy current displacement sensor. The test results are obtained by a data acquisition (DAQ) and restored in a master computer.

Based on the analysis and optimization results, a series of PM-GMM bar samples are manufactured, with different length for GMM and PM patches. The magnetic field intensity of SGMA is acquired by a Hall effect magnetometer and displayed on the Tesla meter; a specific frame is manufactured to monitor the close magnetic circuit. A sample combined three GMMs and four PMs are embedded within the frame. The samples of GMM-PM bars together with the steel frame are exhibited as Figure

Samples of GMM-PM bars for magnetic field intensity tests.

Samples of GMM-PM bars with different GMM numbers

Sample of a GMM-PM bar with steel frame

There is an orifice on the left side of the steel frame; in the practical test, the probe of Hall sensor will pass through the orifice and contact longitudinally with the surface of samples. According to the theory in computational magnetism, the field measured very close to the surface outside the material is equal to the intensity inside [

Magnetic field intensity test result.

According to Figure

Mechanisms for GMM devices operation are fundamentally the process of interaction between multiple physics; its governing equation is therefore the coupling dynamics between electromagnetic field and solid mechanical field. The bridge between above fields is the constitutive relation between magnetization and magnetostriction [

Guided by design and optimization, a prototype is fabricated; there are three GMM patches included in the structure; after optimization, their lengths are 17 mm, 16 mm, and 17 mm, respectively. The photo of GMA is exhibited in Figure

Photo of linear-arrayed GMA prototype.

Displacement test is conducted by exerting a series of DC currents exerted directly on GMA; the test displacement curve and its comparison with simulated curve are detailed in Figure

Test displacement curve and its comparison with simulated curve.

According to Figure

This paper covers the general design and optimization for the bias field of a stack GMA structure applied in novel EHSVs. The analysis methods and results in this paper could be applied in further design of SGMA structure. Some specific contributions and basic conclusion are listed as follows:

Compared with traditional structure, a sufficient bias magnetic field could be exerted using less permanent magnet in SGMA; a multi-GMM case could improve the evenness of bias field distribution in SGMA.

A concise loop model for the bias field of SGMA is established to cover the bias magnetic field distribution in GMM patches. Compared with traditional method, this model provides a concise and flexible way to calculate the uneven field in GMM.

A specific superposition effect of bias field in SGMA is discussed; based on the proposed model, the design parameters are optimized to relieve this superposition effect.

Samples with different GMM and PM numbers are fabricated and a prototype of proposed SGMA is fabricated; its tested magnetic field and displacement meet the practical requirement.

Magnetomotive force provided by PM,

Magnetic reluctance of the rod, H

Magnetic reluctance of the air gap from GMM bar to wall, H

Magnetic reluctance of wall, H

Magnetic fluxes, wb

Magnetic vector potential, wb/m

Magnetic scalar potential, wb/m

Magnetic field in each element, A/m

Average magnetic field, A/m

Total length of GMM patches, m

Total length of PM patches, m

Magnetostriction of GMM

Saturated magnetostriction of GMM

Saturated magnetization of GMM, A/m

Magnetization of GMM, A/m

Section area of GMM rod, m^{2}.

The authors declare that they have no competing interests.

The authors acknowledge the financial support on behalf of National Science Foundation of China (no. 51275525).