Novel Approach for a Hybrid Cushioning System in Running Shoes

based on Halbach Arrays

Philipp Kornfeind

and Arnold Baca

Centre for Sport Science and University Sports, University of Vienna, Auf der Schmelz 6a, Vienna, Austria

Keywords: Running Shoe, Sports Technology, Magnet.

Abstract: A novel design approach making use of purely elastic magnet modules based on Halbach arrays for hybrid

midsole constructions is proposed. Recovery of the surrounding midsole material after compression may thus

be supported. In order to overcome challenges induced by the properties of ferromagnetic materials specific

design principles had to be developed and implemented. In particular, mechanical guidance of the magnetic

elements in vertical direction had to be ensured. FEM simulation has been applied in order to identify

practicable geometrical arrangements of the magnets. Sufficient guiding accuracy was achieved by

developing an effective structure utilizing dual Halbach arrays pivoted at a flat angle to one another using a

common axis of rotation. Prototypes of midsoles and running shoes which utilize the novel technique have

been manufactured. Validation tests revealed significantly higher stiffness of the modified midsoles and a

reduced spring deflection. Biomechanical tests of the modified running shoes are in progress.

1 INTRODUCTION

The use of foamed polymer materials in the midsoles

of running shoes (e.g., EVA, PU) has developed over

decades and, with the introduction of thermoplastic

polyurethane (TPU), has led to a noticeable increase

of performance in terms of rebound properties while

reducing mass at the same time. The combination of

cushioning (viscous) and spring like characteristics

(elastic) make these materials the first choice. The

naturally high impact forces during a heel strike foot

pattern put enormous strain into the cell structure of

midsole materials and inevitably lead to material

fatigue (Chambon et al., 2014). Practical tests show

that selected mechanical parameters such as the

energy return change after just a few hundred

kilometres. With increasing use of running shoes, an

increase in the peak forces that occur during impact

(Baltich et al., 2015) can therefore be seen more

frequently, which is associated with a higher risk of

potential joint damage or other disadvantages

regarding the musculoskeletal system (Agresta et al.,

2022). In this paper, we propose an unconventional

design approach in the form of a purely elastic magnet

module for hybrid midsole constructions, which

https://orcid.org/0000-0002-3476-9665

https://orcid.org/0000-0002-1704-0290

among other aspects has the potential to support the

recovery of the surrounding midsole material after

compression. Furthermore, we hypothesize that the

progressive behavior of the repelling magnets might

interact with the sensorimotor/postural control

mechanism, which in turn might result in higher pre-

activation of the neuromuscular system. All in all, this

approach could help to extend the lifespan of a

running shoe and at the same time to provoke a more

active foot strike technique in running, in which

muscular structures take over part of the cushioning

and thus partially reduce the stress on the involved

joints.

Based on the accumulated experience we share

some insights into the entire development process,

starting with rudimentary considerations about the

design, followed by simulation-based constructions

and handmade prototypes and concluding with first

biomechanical tests in running shoes under laboratory

conditions. The idea for this specific approach came

from a long-standing project partner (Grell M.,

inventor), who was scientifically supported by the

Department of Biomechanics (Section Sports

Technology) of the Institute of Sports Science at the

University of Vienna. The developed technology is

132

Kornfeind, P. and Baca, A.

Novel Approach for a Hybrid Cushioning System in Running Shoes based on Halbach Arrays.

DOI: 10.5220/0011552000003321

In Proceedings of the 10th International Conference on Sport Sciences Research and Technology Support (icSPORTS 2022), pages 132-136

ISBN: 978-989-758-610-1; ISSN: 2184-3201

already protected by patents. Alternative use cases

other than running shoes are currently discussed.

2 WHY MAGNETS?

The forces acting on the shoe during running as well

as the high number of load cycles put a strain on the

underlying construction which usually lead to varying

degrees of material fatigue over the long term. In

order to reduce this undesired effect somewhat, we

resorted to the principle of repelling magnets (high

graded neodymium) in our approach. When two

permanent magnets with the same polarity come

together, opposite forces (repelling forces) with

progressive spring characteristics are generated. The

compression phase takes place without any physical

contact between the two elements (air gap) and thus

enables an enormously high number of cycles without

any noticeable weakening of the elastic properties

compared to foam materials.

2.1 Halbach Arrays

A special arrangement of single dipole magnets in a

predefined sequence (the so called “Halbach array”;

Halbach, 1980) enables the usually symmetrical

formation of the magnetic field to be extensively

shifted, resulting in an asymmetric dipole with a

stronger and a weaker side (Figure 1). The individual

Figure 1: Example of magnetic field distributions for

uniaxial aligned magnets vs a Halbach array (FEMM 4.2).

magnets are aligned with each other in alternating

orientation (e.g. 5 segments in 0 | 90 | 180 | 270 | 0

deg. of angular direction) and combined to form an

array.

The combination of two such arrays aligned on

their stronger sides in one construction enables an

enormous increase in the resulting repulsion forces.

Similarly, the Halbach array structure allows a

reduction in the materials used with the same effect

in terms of repulsive forces. In principle, the desired

spring curve can be specifically adjusted by varying

certain construction parameters (number of magnets,

dimensions, geometry) and adapted to individual

needs (customized technology).

2.2 Challenges

In addition to positive aspects such as increased

service life (no fatigue effects) or faster rebound (no

damping), this approach also entails additional

challenges. Ferromagnetic materials have a much

higher density compared to foamed materials (about

7.5 g/cm³ vs. 0.25 g/cm³) and would significantly

increase the total mass of a running shoe even with

low material usage. Therefore, a possible use should

be locally limited and in any case be in functional

coordination with the entire running shoe. The spatial

conditions in the area of the midsole needs also to be

considered (shape and maximum height).

From a design point of view, one of the most

important aspects when using magnets is to ensure

mechanical guidance in the vertical direction when

two magnets approach each other. Without this, an

unwanted lateral evasive movement would

immediately occur, reducing the intensity of the

repulsive forces. When using Halbach arrays, there is

also the risk that shifts beyond a segment width will

result in a reversal of the effect (instead of a repulsive

effect, both arrays will strongly be attracted).

2.3 FEM-Simulation

In order to be able to better estimate the influence of

different geometry, arrangement (iteration step size)

and number of segments on the repulsion effect,

numerous simulations were carried out with a free

simulation software (FEMM 4.2). The specific

material characteristics (required for the simulation of

the magnetic fields) could be obtained from various

data sheets from manufacturers and distributors (K&J

Magnetics). Specifically, a simulated compression of

two arrays with an assumed air gap (10 mm) up to

complete contact (0 mm) was calculated. In addition

to the respective formation of the magnetic fields, the

Novel Approach for a Hybrid Cushioning System in Running Shoes based on Halbach Arrays

133

results also provided the resulting vertical forces at a

certain distance (air gap). In this way, spring

characteristics of different variants could be

compared and an optimized version identified with

regard to their effect in combination with the

respective mass (Figure 2a).

Figure 2: (a) Simulation results of different Halbach array

variants (force vs. distance). (b) Interaction between two

Halbach arrays of the final version (7 segments).

The finally selected magnet had a cuboid

geometry with the dimensions 4x4x10 mm (height x

width x depth) and consisted of an N52 graded

neodymium material with a nickel coating. For a

single Halbach array, a total of 7 segments have been

combined in an alternating sequence with an offset

angle of 90 degrees each. In any case, the individual

segments have to be fixed in their position, since the

naturally developed magnetic flux of a dipole would

lead to displacements under the magnets. This can

basically be accomplished by gluing into a template

or by press fitting into a predetermined fixture.

3 DESIGN, CONSTRUCTION

AND MANUFACTURING

At the beginning of the project, numerous preliminary

considerations, sketches and test setups were made

for possible arrangements of two Halbach arrays and

for the selection of materials. The most challenging

was the low overall height (assumption: max. 15mm)

as well as the realization of the necessary guidance

accuracy (assumption: horizontal deviation <10%).

This challenge can be overcome either through form-

fitting connections of the surfaces involved (e.g. two

components sliding into each other) or with or with

the help of vertical guide rails and tilt-resistant guide

bushes.

When two components are connected in a form-

fitting manner, displacements inevitably lead to

friction losses on the contact surfaces. As a

consequence of the high number of repetitions to be

expected, there is also unwanted material abrasion as

a sign of wear. On closer inspection, the second idea

also did not appear to be entirely practical, as it could

be prone to tilting during compression and rebound.

As an alternative, another possibility was therefore

developed in which the two arrays can be pivoted at a

flat angle to one another using a common axis of

rotation (e.g. hinge joint). In order to improve the

effectiveness, the idea of a mirrored structure was

born in which two double arrays work together (see

Figure 3).

Figure 3: Final draft for the design of the magnetic module

with dual Halbach arrays (frontal & perspective view).

This variant is less sensitive to decentralized force

application (COP) and, according to the simulation,

achieves a maximum repulsive force of about 230 N

(fully compressed, air gap = 0 mm) with a total mass

of less than 50 g. In coordination with the surrounding

material and due to the limited installation height, a

design-related preload of 50 N was implemented with

a remaining deflection of almost 6 mm.

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The complete implementation was carried out

using a commercially available CAD program

(SOLIDWORKS®). Additional FEM simulations

have been conducted to obtain the necessary material

specifications. The high material requirements in

terms of rigidity and strength led us to opt for a highly

rigid carbon fiber reinforced plastic (20% CF

filament). During construction, attention was paid to

the compatibility of the components with regard to

3D printing and the accuracy class of our production

options (minimum layer thickness 100 m). Spring

steel with a diameter of 1.5mm was selected as the

common axis, and the individual elements for holding

the magnets were produced using a 3D FDM printing

process (Ultimaker S5 Pro Bundle).

Figure 4: (a) Manual assembly (b) one finished module.

The assembly was done by hand and the

individual segments were glued together with

cyanoacrylate (superglue). The individual elements

were fitted with the magnets and then strung in the

specified order on the common axis of rotation and

also on stabilizing carbon rods at the outer ends

(Figure 4). The manufactured module was subjected

to simple function tests (application of mechanical

loads) and series of measurements were carried out

using a force measuring platform, which

substantiated the simulation results (spring

characteristics).

4 VALIDATION

4.1 Artificial Tests

As mentioned in the introduction, the innovative

magnet module is to be used specifically in

combination with surrounding midsole materials. For

functional tests, a test specimen (e.g. made of foamed

EVA) with a suitable mount for a module is required.

To produce this, cuboids were cut out (70 x 70 mm,

20 mm thick) and the negative form of a complete

module was milled using a CNC milling machine

(Figure 5). The specimen was designed to be

subjected to dynamic tests on a professional hydraulic

test stand with standardized stamps (imitation of the

human heel geometry). In this case, cyclically

repetitive impact movements are carried out at a

defined ingress/egress speed and the reaction force

acting on the contact surface is measured.

Figure 5: Specimens for test trials.

The midsole materials used in running shoes are

usually tested on the basis of such test series and

examined with regard to rebound, cushioning and

material fatigue (Schwanitz et al., 2010).

Within an international cooperation, we were able

to have some test series performed with the

previously mentioned test stand in order to make a

direct comparison between the hybrid variant and the

unmodified material. 1000 cycles at a frequency of

1.4 Hz (corresponds to a simulated running speed of

about 10 km/h) with a maximum vertical force of

1000 N were applied to the respective test specimen.

In the results, we concentrated on cycle #100

(material warm-up) and #1000 (first material fatigue)

and calculated, among other, parameters for assessing

energy loss and stiffness (Figure 6).

Figure 6: Test results (hysteresis) for the hybrid-specimen

and unmodified EVA material for cycle #100 and #1000.

The unmodified variant shows the first signs of material

fatigue (reduction in stiffness, increased energy loss) after

just 1000 cycles, while the hybrid version remains very

stable in this respect.

As can be seen quite clearly, the progressive

spring characteristic of the magnet module has a

Novel Approach for a Hybrid Cushioning System in Running Shoes based on Halbach Arrays

135

strong influence on the overall structure (test

specimen + module). In a direct comparison, the new

approach shows a significantly higher stiffness, but in

combination with a reduced spring deflection (due to

the incompressible elements). Based on the changes

over time after 1000 cycles, the results in terms of

energy return are on a similar level. Surprisingly,

there is a slight trend towards more rigidity in the

hybrid construction, while the EVA material loses a

little in rigidity.

4.2 Biomechanical Tests

A first pilot study to evaluate the possible effects of a

magnetic module in a conventional running shoe is

currently being carried out. A pair of running shoes

was modified in such a way that the midsole material

was separated between the heel bone and the

longitudinal arch to accommodate one module each

(Figure 7). The second pair of running shoes

remained unchanged. Subjects participating in our

experiment are asked to run with both variants after a

few minutes of warm-up, at a controlled running

speed (endurance pace) over force measuring plates

mounted into the ground. In addition to the ground

reaction forces, we record EMG data in selected

muscle groups of the lower extremities.

The aim of this pilot is to identify possible

interaction effects both in terms of dynamics and

neuromuscular activation and to observe individual

responses (responders vs. non-responders).

Figure 7: Modified prototype of one selected model of

running shoes for biomechanical performance tests and

comparison to unmodified version.

5 CONCLUSIONS

Using the latest construction methods (FEM

simulation, CAD design, rapid prototyping), a new

type of magnetic spring suitable for running shoes has

been developed and manufactured. The thereby

created novel module was compared and evaluated in

several test series and confirmed our expectations. A

pilot study currently being carried out focuses on the

practical suitability for use in common running shoes.

We expect further results on efficiency, design issues

and acceptance, which might also help in transferring

the magnetic technology to other areas than running.

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