SHEFFIELD HALLAM UNIVERSITY FACULTY OF

1 2 3

SHEFFIELD HALLAM UNIVERSITY

4

FACULTY OF HEALTH AND WELLBEING

5 6

MODULE 66-7267-00N

7

RESEARCH PROJECT MANUSCRIPT

8

Experimental and finite element analysis of a shuttlecock under static and dynamic loads.

9 10

July 2017

11 12

Submitted by

13

Michael Thelwell

14 15

STUDENT ID: 26034770

16

[email protected]

17

Supervisor:

18

Dr. John Hart

19 20

WORD COUNT: 4456

21

FIGURE COUNT: 6

22

TABLE COUNT: 2

23 24

in partial fulfilment of the requirements for the degree of

25

Master of Science in Sports Engineering

INDUSTRY LINKED PROJECT: 66-7267-00N

Michael Thelwell: 26034770

26

Abstract

27

This paper presents an investigation of impact deformation characteristics of badminton shuttlecocks using

28

experiment and Finite Element Analysis. Due to the unique form and structure of a shuttle skirt, complex

29

structural deformation occurs upon impact and rebound where the shuttle recovers form. Although shuttle

30

flight has been investigated, little research exists regarding shuttle impact mechanics, and as such is an area

31

that is still not fully understood. Deformation of two designs of synthetic shuttle were assessed under static

32

and dynamic loads. Dynamic loading was digitised from high speed video capture of shuttles obliquely

33

impacting a rigid surface. Static loading involved application of known mass at specific skirt locations to

34

recreate typical deformation scenarios, and digitisation of captured still images to determine deflection.

35

Modelled shuttle geometry was based upon an Artengo BSC800 synthetic shuttle. The FE model was used

36

to simulate deformations of a synthetic shuttle skirt resulting from static loading and was compared against

37

experimental data. Synthetic shuttles were observed to exhibit compensatory deformation characteristics,

38

due to the continuous circumferential nature of synthetic skirts. This causes large-scale deformations to

39

translate around the entire skirt rim under both dynamic and single point loading. Also, it has been shown

40

that increases in inbound velocity and angle lead to a greater collapse of the shuttle skirt during impact with

41

a surface, characterised by a reduced vertical COR. The FE model could recreate the overall compensatory

42

deformation characteristics of a shuttle under static loading. However, there were errors between the

43

experiment and simulation.

44 45

Keywords: badminton, shuttlecock, finite-element analysis, impact, deformation

46 47 48 49 50

2


51


1. Introduction

52

A badminton shuttlecock is an entirely unique sports projectile, both in form and mass (Hart, 2014). As a

53

result, shuttles experience complex structural deformation during the dynamic impact phase, but also

54

exhibit some deformation during the often considered structurally static flight state, in a manner that is still

55

not fully understood. Previous research into shuttle behaviour is limited and has focused largely on the

56

aerodynamics of steady state flight (Cooke, 1999; Alam, Chowdhury, Theppadungporn, & Subic, 2010;

57

Hart, 2014). Therefore, analytical and predictive models of shuttlecock flight do exist, however, they do

58

not account for the structural deformation of shuttles during the impact and rebound phase in any manner

59

and is an area that remains largely unknown (Lin, Chua, & Yeo, 2013). The only previous investigations

60

into shuttle impact mechanics are that of Cooke (1992) and Lin et al. (2013), who both stated that further

61

research on shuttle deformation needed to be carried out before it could be fully understood. Although these

62

studies have provided a basis of understanding of shuttle deformation during impact, there are currently no

63

objective measurements or predictive models of shuttle behaviour that might enable researchers to fully

64

understand this phenomenon.

65

Feather shuttlecocks are still considered the gold standard for badminton competition (Cooke, 1992; Lin et

66

al., 2013), but due to their rapid structural degradation and an increasing shortage of feathers available for

67

use in shuttle manufacture, they are relatively expensive with a short lifespan. Thus, synthetic shuttles began

68

being developed as a more durable and economical alternative (Cooke, 1992; Alam, Nutakom, &

69

Chowdhury, 2015). The rachis of a bird’s feather is a composite keratin structure, which is filled with a

70

foam-like core formed by medullary cells that aids the outer cortex to resist buckling, making it extremely

71

stiff and lightweight (Bachmann, Emmerlich, Baumgartner, Schneider, & Wagner, 2012). Synthetic shuttle

72

manufacturers have so far been unable to replicate these stiffness properties in their products, made from

73

injection moulded polyamide materials, meaning that there is currently no synthetic shuttle that has the

74

same feel and deformation characteristics as a feather shuttle (Cooke, 1992). Understanding the impact

75

performance and deformation characteristics of synthetic shuttles is the focus of this study.

3



76

Much of the previous work studying sports balls, most notably in tennis, golf and softball (Nevins & Smith,

77

2015) has resulted in the development of models, of varying complexity, to describe and predict their

78

impacts with a surface or an implement (Goodwill, Kirk, & Haake, 2005). Analytical models of increasing

79

complexity range from Newtonian models (Daish, 1972) to visco-elastic models (Goodwill & Haake,

80

2004). Though these can provide a suitable first approximation of ball deformation and are often in good

81

agreement with experimental data they cannot simulate the complex 3D deformations that projectiles

82

experience during impact due to assumptions that must be made (Goodwill et al., 2005). Therefore, to gain

83

a better understanding of impact mechanisms, more advanced finite element (FE) models can be developed

84

(Goodwill et al., 2005). FE models, though still a simplification, can be used to simulate complex, non-

85

linear and time-dependent deformations of sports projectiles, which cannot be found easily by experimental

86

methods (Mehta, 1991). The use of FE models in sports involving projectiles, such as tennis (Goodwill et

87

al., 2005) and golf (Tanaka, Teranishi, & Ujihashi, 2012), has developed researchers’ understanding of the

88

impact mechanics and informed the design of new and improved products for those sports.

89

This paper presents an experimental validation of impact and the first stages of an FE investigation,

90

presenting results for a synthetic shuttle to develop current understanding of shuttle impact deformation

91

and provide a method for optimising future synthetic shuttle design. The work in this paper is presented in

92

two distinct sections. The first presents experimental data for oblique impacts of synthetic shuttles against

93

a rigid surface, to develop understanding of the types of deformation that can be expected during dynamic

94

impact and turnover. The second section discusses the development and verification of an FE model of a

95

synthetic shuttle. Verification of the FE model was conducted via the application of static loads, ensuring

96

that the model could reliably recreate a simplified load case before the simulation of more complex dynamic

97

loads as seen during impact.

98 99 100

4


101


2. Methods

102

The methodology to achieve the previously stated aims is presented in the following stages:

103

1. Dynamic testing of a synthetic shuttle against a rigid surface to understand typical skirt deformations.

104

2. Static loading of a synthetic shuttle to replicate skirt deformations for use in FE model validation.

105

3. First stages of an FE investigation of a synthetic shuttle.

106

2.1 Dynamic impact testing

Shuttlecock

Badminton player with racket.

Rigid surface Vitec multiLED light

107

Phantom MIRO 110BW HSV

Vitec multiLED light

Figure 1. Experimental setup for high speed video capture of oblique impacts against a rigid surface from side-on viewpoint.

108

Deformations of two synthetic shuttles (Artengo BSC800 & Yonex Mavis 370) during an oblique impact

109

against a rigid steel surface were investigated. Impacts were against a rigid surface rather than a racket

110

string bed to isolate the shuttle skirt deflection, without having to consider the complexity of string bed

111

dynamics at this early stage of the FE models development. The equipment used in this experiment is shown

112

in Figure 1. As shown, shuttles were hit with a badminton racket onto a rigid surface by a high-level

113

university badminton player. The participant in this study had previously competed at collegiate level and

114

could hit shuttles consistently over a range of inbound velocities representative of typical shuttle-racket

115

impacts. Impacts were captured using a Phantom MIRO 110BW HSV camera recording at 1600 fps, which

116

enabled quantitative measurements of dynamic impact behaviour. Additional lighting was provided by two

117

Vitec multi-LED spotlights to allow for high-speed recording. Impacts were recorded from both side on

118

and head on viewpoints to fully capture the deformation characteristics of the shuttle skirt. Inbound and 5



119

outbound shuttle velocity, angle to the horizontal surface, vertical coefficient of restitution (COR) and skirt

120

deflection were found from manual digitisation of high-speed video footage using Check 2D kinematic

121

analysis software (Version v1.5.0; CSER, 2017). Pearson’s correlation coefficient was calculated to

122

investigate relationships between shuttle trajectory variables and skirt deformation characteristics.

123

2.2 Static loading of a synthetic shuttle skirt

124

The purpose of performing static loading was that in order to effectively develop the FE model of the

125

shuttle, typical deformation scenarios for the lower skirt region seen during impact must initially be

126

simplified to a static case. Once deformations due to static loading on the FE model can be verified as being

127

in agreement with experimental data, then further complexity can be added in the form of dynamic loads,

128

as seen in the oblique impact testing. Static loading consisted of hanging known mass at four specific skirt

129

locations around the circumference of a horizontally clamped shuttle, shown in Figure 2. These specific

130

load locations were selected as a way of recreating typical deformation scenarios in the lower skirt region

131

observed during dynamic impact testing against a rigid surface. Deformations of two synthetic shuttles were

132

investigated (Artengo BSC800 & Yonex Mavis 370). Deflection of the shuttle skirt was determined from

133

digitisation of captured still images at each stage of loading and unloading. Applied mass was increased

134

incrementally in a quasi-static manner from 0 g up to a maximum of 92.06 g, depending on load location,

135

to assess the skirts deflection. The data collected from this stage would be used to validate the FE model

136

during a basic validation of material and structural performance during static loading.

1 3 4

mg

L

137 138 139

2

Figure 2. (a) Static loading experimental setup (L - length of shuttle skirt; mg - weight of static load); (b) Load locations (1 upper vertical; 2 - lower vertical; 3 - 45 degrees; 4 - 90 degrees).

6



2.3 Finite element model of a synthetic shuttlecock

141

2.3.1 CAD geometry

142

Modelled shuttle geometry was based upon an Artengo BSC800, a practice-grade synthetic shuttle and was

143

constructed in SOLIDWORKS 3D CAD software, shown in Figure 3. All shuttle measurements were made

144

using digital verniers, and a digital vernier height gauge on a granite measurement slab. Repeat

145

measurements were taken radially to capture all fine skirt details of the shuttle. The shuttle was measured

146

to have height H = 77.4 mm, maximum skirt diameter D = 68.5 mm and total mass of 5.26 g, of which the

147

shuttle skirt accounted for 2.86 g.

Upper Skirt

Base

140

Lower Skirt

H

148

D

149

Figure 3. (a) Artengo BSC800 shuttle; (b) Shuttle CAD model; (c) Shuttle FE computational mesh.

150

2.3.2 Solver

151

The finite element model was created using the commercially available ANSYS Mechanical FE code and

152

all simulations were run using the ANSYS Mechanical APDL solver to perform a nonlinear static structural

153

analysis. All simulations were performed on a Z230 HPC with an i7 4790 Quad-Core processor using 4

154

processing cores.

155

2.3.3 Mesh

156

A mesh dependency study was carried out as part of the FE model validation to assess the sensitivity of

157

numerical solution to mesh resolution. The results for this are shown in Table 1 in the following section. A

158

range of computational meshes were created for the FE model, which consisted of discrete tetrahedral

159

elements, shown in Figure 3. 7



160

Static loads were applied to the modelled skirt at each of the four load locations, shown in Figure 2, to

161

verify that deflections of the FE model matched those of a synthetic shuttle collected in experiment.

162

Deflection of the modelled skirt was determined from deformation probes placed at each load point and

163

locations around the skirt. To apply load to the FE model skirt in the same incremental quasi-static manner

164

that known mass was added during the experiment, sub-steps of 30 seconds were defined to specify a

165

transient load history curve for the model. Applied load was added to the FE model in the same increments

166

as during the experiment at each of these time-steps so that a more accurate solution could be obtained from

167

the simulation. Additional boundary conditions for this simulation included the application of a fixed

168

support on the shuttle base, as well as alignment of the shuttles length along the z-axis, therefore simulating

169

the shuttle being horizontally clamped as seen during experimental loading (Figure 2).

170

2.4 Validation of FE model

171

Validation was key to this investigation, since if there was good agreement between the results of the

172

simulation and the experimental data, we could gain confidence in the model and use it to simulate more

173

complex dynamic load scenarios in future. Validation of the FE model considered the influence of both the

174

computational mesh and the effect of material properties on the results of simulating static loading.

175

2.4.1 Mesh

176

Three mesh iterations were constructed for the shuttle, with densities ranging from 305,415 elements

177

(minimum element size 0.3 mm) up to 1.26 million elements (minimum element size 0.15 mm). Significant

178

changes in mesh density were made between each iteration to ensure that the solution was truly converging

179

(Table 1), since only small changes in mesh size can produce results that can be misinterpreted as

180

convergence. During the mesh dependency study, the maximum load applied to the upper vertical position

181

in the experiment was used for simulation. Empirically, this caused the Artengo shuttle skirt to deform

182

vertically by 28.63 mm at the load location. To ensure that the FE model was computationally economic

183

for the purposes of this simulation, total time to reach a solution and element quality were considered. The

184

reduction of minimum cell size improved overall element quality, with this value ideally being close to 1.

8



185

2.4.2 Material Properties

186

Synthetic shuttle skirts are most commonly made from a polyamide material, such as nylon. There are many

187

types of nylon commonly used in manufacture, with higher number nylons having increased moisture

188

content and therefore reduced strength and stiffness properties. Furthermore, synthetic shuttle

189

manufacturers use different additives to improve their material properties and performance. Therefore, the

190

exact grade of nylon used in the Artengo shuttle being modelled was unknown. For this study, nylon 11

191

was selected for the material model, since it is commonly used in the manufacture of sports products and

192

its material properties are available in online data sheets (Matweb, 2017). To more accurately model the

193

plastic behaviour of the synthetic shuttle skirt, a nonlinear analysis was required, since an approximation

194

of linear behaviour would drastically affect the results of a numerical simulation. Loads were applied at the

195

upper vertical position using both a linear and a nonlinear approach to assess the effect of a linear

196

approximation on the performance of the model. Previously collected experimental data of stress-strain

197

relationships for nylon (Soleimani & Saadatfar, 2012) were added to the material model, enabling ANSYS

198

to more accurately simulate the nonlinear deformation of the shuttle skirt during a load cycle.

199

Table 1. Computational Mesh. Mesh Iteration

Linear/ Nonlinear Material

Max. Element Size (mm)

Min. Element Size (mm)

No. of Elements

Deformation at load point (mm)

Error from Experiment (mm)

Element Quality

Elapsed Solving Time

1

Linear

1

0.3

305,415

13.57

15.06

0.70234

1 min 10 secs

1

Nonlinear

1

0.3

305,415

23.31

5.32

0.70234

9 min 24 secs

2

Nonlinear

1

0.2

558,857

23.74

4.89

0.74733

2 hours 44mins

3

Nonlinear

1

0.15

1,261,572

24.04

4.59

0.77447

3 hours 32 mins

200

From the mesh dependency study, a nonlinear material model was chosen, since it drastically reduced the

201

amount of error between the simulation and experiment for deformations caused by static loads at the upper

202

vertical position. Also, the final mesh selected for the FE model was iteration 3, since this produced the

203

lowest error from the experiment in terms of skirt deformation and had the highest element quality. Any

204

further increases in mesh density only caused small changes in measured skirt deflection, but the total

205

solution time increased dramatically.

9


206


3. Oblique impact of a synthetic shuttle on a rigid surface

207

Screenshots of shuttle deformations following an oblique impact for both the Artengo BSC800 and the

208

Yonex Mavis 370 synthetic shuttles are presented in Figure 4. The time interval between each image in the

209

sequence is 0.000625 seconds. Observations of deflections from each of the two viewpoints highlighted

210

different features of shuttle impact characteristics. The head-on view (Figure 4a) shows the intricate

211

deformations that translate around the entire skirt rim following impact. While the side-on view (Figure 4b)

212

shows overall deflection of the skirt relative to the shuttle base, as well as the overall collapse of both the

213

upper and lower skirt sections. Skirt deflections from each of these viewpoints are analysed in turn. (a)

(b)

214 215 216

Figure 4. Deformations of shuttle skirts following an oblique impact with a rigid surface; (a) Head on view of Artengo synthetic shuttle; (b) Side view of Yonex synthetic shuttle.

217

Figure 4a shows the dramatic deformations of the lower skirt section and how it oscillates during the initial

218

stages of turnover. These deformations cause the diameter of the shuttle skirt to either increase or decrease,

219

due to the lower skirt stretching outward or folding inwards, respectively. It was also found that an increase

220

in skirt diameter in one direction was accompanied by a greater decrease in diameter perpendicularly at the

221

same instant. For example, following an impact of the Artengo shuttle, the skirt diameter had

222

simultaneously increased by 6.4 mm in one direction and decreased by 30.7 mm in the perpendicular

223

direction. Then in a subsequent frame, the skirt diameter had simultaneously decreased by 9.5 mm in the

224

first direction and increased by 1.9 mm in the perpendicular direction. These compensatory deformations

225

are most likely due to the continuous circumferential nature of synthetic shuttle skirts, which causes these

10



226

large-scale deformations to translate around the entire skirt rim following impact. In addition, the shuttle

227

skirt is stronger in resisting outward deflection than inward deformation because of inbuilt reinforcing

228

structures, on the internal surface of the lower skirt. From HSV, these dynamic oscillations of the shuttle

229

skirt were found to last up to 0.0125 seconds following impact, depending on inbound velocity.

230

From the results in Figure 5 and Table 2, vertical inbound velocity and angle to the horizontal prior to

231

impact were found to have a large effect on both the measured vertical COR and deformation experienced

232

by the skirt of both grades of shuttle. Vertical COR for an oblique impact is defined as the ratio of the

233

rebound and inbound velocity components that are perpendicular to the surface. It was found that the steeper

234

the inbound angle and therefore the higher the vertical component of inbound velocity of the shuttle, the

235

lower the vertical COR for the impact. These results agree with those of previous studies for tennis

236

(Goodwill et al., 2005) and golf (Arakawa et al., 2006) ball impacts with a rigid surface. The relationship

237

between vertical COR and inbound angle measured for all shuttle impacts was found to have a Pearson’s

238

correlation coefficient, r = -0.88 and coefficient of determination, R2 = -0.78, indicating a strong negative

239

correlation between these variables. This gives confidence to the accuracy of measurements made during

240

digitisation. Also, it was shown that the steeper the inbound angle, the greater the amount of deformation

241

experienced by the lower skirt section following impact. Therefore, it follows that a steeper inbound angle

242

causes a greater collapse of the shuttle skirt during impact, leading to higher hysteresis losses, which is

243

characterised by a lower vertical COR. Artengo impact (A1), shown in Figure 5, highlights the practical

244

implications of this phenomenon. It had the steepest inbound angle, the lowest vertical COR value and

245

experienced the largest in-plane deformation of all measured impacts. Interestingly, during this impact the

246

shuttle was orientated so that the skirt contacted the surface, similar to how a shuttle might impact a racket

247

during a typical shot in badminton, as observed by Lin (2013). This could explain why players perceive

248

synthetic shuttles to feel ‘heavy’ during impact with the racket, since this type of impact is characterised

249

by a lower COR and slower rebound of the shuttle.

11



A1

A2

Y1

Y2

A3

Y3

250 251

Figure 5. Deformations for three Artengo (A1-A3) and three Yonex (Y1-Y3) synthetic shuttles during an oblique impact.

252

Table 2. Measurements for an Artengo and Yonex synthetic shuttle during an oblique impact with a rigid surface.

Shuttle Type Artengo BSC800 Yonex Mavis 370

Shot No.

Inbound Angle (o)

Resultant Inbound Velocity (m s-1)

Vertical Inbound Velocity (m s-1)

Vertical COR

Max. Decrease in Skirt Diameter (mm)

Max. Increase in Skirt Diameter (mm)

A1

53.18

24.91

19.96

0.55

36.97

2.30

A2

42.47

20.02

13.54

0.58

15.60

4.95

A3

37.50

16.00

9.83

0.62

11.28

4.11

Y1

42.79

23.74

16.17

0.60

20.94

6.75

Y2

41.48

21.99

14.31

0.61

21.72

6.44

Y3

33.66

22.05

13.57

0.61

11.28

4.51

253

The final Yonex impact (Y3), displays another interesting phenomenon. Y3 had the lowest inbound angle

254

of the measured impacts, and therefore had a lower vertical inbound velocity relative to its resultant

255

velocity. As shown in Figure 5, this resulted in significantly higher levels of deformation of the upper skirt

256

section compared to the other impacts, where most of the observed deformation had been in the lower skirt

257

section. This caused an s-shaped deformation of the shuttle, which propagated throughout the length of the

258

shuttle skirt, as was observed by Cooke (1992) for shuttle impacts with a racket. This altered form of

259

deformation of the skirt may be due to an increased horizontal deceleration of the shuttle base on the rigid

260

surface, resulting from the decreased inbound angle. This increased deceleration of the base could be

261

inducing a rolling effect on the shuttle skirt, similarly to how a ball would rebound from a surface and

262

generate spin during an oblique impact (Goodwill et al., 2005). Further research of this phenomenon is

263

required to understand it fully. 12


264


4. Validation of FE model

265

The results of static load testing show that deformations caused from single point loading match those

266

observed during dynamic impact testing very closely. Specifically, outward deformation of the skirt in one

267

direction was accompanied by a simultaneous inward deflection in the perpendicular direction around the

268

skirt circumference. These compensatory deformations of the skirt are due to the continuous circumferential

269

nature of synthetic skirts causing large scale deformations to be translated around the entire skirt rim under

270

all loading scenarios. This confirmed that performing static loading to recreate deformations from dynamic

271

loading of the shuttle skirt was a valid method of performing an initial validation of the FE model.

272

Figure 6 shows results of the static load testing for both synthetic shuttles (Artengo & Yonex) and simulated

273

loading of the FE model at each load location, as well as comparisons of the overall deformation

274

characteristics caused by the application of static loads, both in experiment and simulation. Mixed levels of

275

agreement were found between the experiment and the FE model, depending on where the load was applied.

276

Figure 6a shows that the FE model was in good agreement with experiment for deformation at the upper

277

vertical load location and in the principal perpendicular deformation direction around the skirt

278

circumference. Similarly, Figure 6c shows that the FE model was in good agreement with experiment for

279

deformation under maximum loading at the 45-degree load location. However, though the FE model

280

deformed in the perpendicular direction at the same location as in the experiment for the 45-degree loading,

281

it over predicted the amount of deformation in this direction. For both the upper vertical and 45-degree load

282

scenarios (Figures 6a & 6c), deflections of the FE model were found to be overly localised at the load

283

location. Only a small section of skirt adjacent to the load was deforming inward, rather than large sections

284

of the skirt folding inwards, as observed during experimental loading. This meant that the overall

285

compensatory deformation characteristics observed in both the dynamic and static testing were not

286

recreated fully by the FE model. These differences in deformation are most likely due to simplifications

287

made to the shuttle geometry during development of the FE model.

13



(a) Experiment - Yonex Experiment – Artengo × Simulation

(b) Experiment - Yonex Experiment – Artengo × Simulation

(c) Experiment - Yonex Experiment – Artengo × Simulation

(d) Experiment - Yonex Experiment – Artengo × Simulation

288

Figure 6. Comparisons between the undeformed state (blue line), skirt deflections for two synthetic shuttles (Artengo & Yonex) in the experiment (red line) and the ANSYS finite element model (image) from static loading at each of four load locations; (a) Upper Vertical; (b) Lower Vertical; (c) 45 degrees; (d) 90 degrees.

14



289

Figures 6b & 6d show reduced agreement between the FE model and the experiment for deformations at

290

the load point at the lower vertical and 90-degree load locations. Deformation at the lower vertical location

291

in the FE model matched that of the experiment at low loads, but as the applied load increased the FE model

292

increasingly over-predicted levels of vertical deformation at the load point compared to the experiment.

293

However, levels of perpendicular deformation around the skirt caused by loading at the lower vertical

294

position showed better agreement between the FE model and the experiment, shown in Figure 6b. Similarly,

295

Figure 6d shows good agreement between the FE model and experiment for deformations at the 90-degree

296

load position at low loads. However, in the experiment the shuttle skirt experienced a dramatic inward

297

folding with approximately 0.5 N of applied load, a phenomenon which was not recreated in the FE model

298

during simulation, resulting in less agreement for the entire load cycle. Also, levels of perpendicular

299

deformation elsewhere on the skirt caused by the 90-degree loading scenario showed good agreement

300

between the FE and the experiment. The skirt not only deformed outwards in the same primary location in

301

the FE model as in the experiment, but was also of the correct order of magnitude. However, similarly to

302

the upper vertical and 45-degree load scenarios, the overall compensatory deformations seen in experiment

303

were not fully recreated by the FE model during loading at the 90-degree position. Again, this is most likely

304

due to inaccuracies in modelling the strengthening structures present in a synthetic shuttle.

305

Key reasons that deformations of the FE model did not perfectly match those observed during the

306

experiment include: simplifications of the CAD geometry and the material properties of the Artengo shuttle

307

skirt being unknown. The modelled shuttle geometry was created to include as many fine skirt details as

308

possible. However, as is common in simulation, simplifications were made to allow for subsequent meshing

309

of the FE model. This led to certain strengthening structures that are moulded into a synthetic skirt not

310

being represented completely, which may have affected the results of the simulation. In addition, these

311

simplifications also led to a difference in mass between the Artengo shuttle and the shuttle model. The

312

Artengo shuttle skirt had a recorded mass of 2.86 g, whilst the modelled shuttle skirt had a predicted mass

313

of 2.15 g calculated within SOLIDWORKS 3D CAD software. This difference in mass could have had a

15



314

considerable effect on the levels of deformation simulated in the FE model. The material properties gathered

315

from online data sheets, which were used to define the material model, may not have matched those of the

316

Artengo BSC800 shuttle. This will have caused reduced agreement between the FE model and the

317

experiment for deformations of the shuttle skirt due to static loading, since any differences in material

318

properties, such as: density, Young’s modulus, tensile strength as well as stress-strain relationship will

319

influence how a material behaves under loading. Nevertheless, the results of this initial FE investigation

320

are encouraging. Although the skirt in the current model does not deform the same distance as in experiment

321

at all load points, it does deform in the correct manner. This gives us confidence that the overall structure

322

of the shuttle FE model is correct, but due to differences in material properties, as well as simplifications

323

in geometry it currently does not deform the same as a real shuttle under static loading.

324

Recommendations for further research in this area include: development of the current shuttle CAD

325

geometry that more accurately replicates the strengthening structures present within a synthetic shuttle.

326

Also, more comprehensive collection of material properties, which represent those of a synthetic shuttle.

327

This could be achieved by conducting tensile and compressive mechanical testing on several material

328

samples of processed/injected nylon, with a range of manufacturing additives, of the same thickness as a

329

synthetic shuttle skirt. This would enable several multilinear stress-strain relationships to be plotted and

330

simulated within the shuttle FE model to achieve improved agreement with experimental data for static

331

loading. In addition, further investigations should be conducted with regards to dynamic loading of a shuttle

332

against a rigid surface. In the present study, only oblique impacts against a surface were considered, though

333

as was shown in the results of dynamic testing, the deformation characteristics of a shuttle depend greatly

334

on its inbound trajectory and its orientation with the surface upon impact. Therefore, more data from oblique

335

impacts should be collected to confirm the phenomena observed in the present study, as well as for normal

336

impacts with a surface to see the effects on skirt deflection. Once the impact dynamics of a shuttle are fully

337

understood for impacts with a surface and a model has been verified as being able to simulate those complex

338

deformation characteristics, investigation of shuttle impacts with a racket can then be conducted.

16


339


5. Conclusions

340

An initial finite-element investigation of a synthetic shuttle has been conducted to improve current

341

understanding of synthetic shuttle deformation characteristics under static and dynamic loads. Experimental

342

data has been collected which quantifies the levels of skirt deflection that occur due to dynamic loading

343

from an oblique impact with a rigid surface and from static single-point loading. From the results, it has

344

been shown that an increase in inbound velocity and angle leads to a greater collapse of the shuttle skirt

345

during impact with a surface, characterised by a reduced vertical COR. Also, it was found that synthetic

346

shuttles display compensatory deformation characteristics, due to the continuous circumferential nature of

347

synthetic skirts. This causes large-scale deformations to translate around the entire skirt rim under both

348

dynamic and single point loading. An initial FE model was created to simulate the 3D deformation of a

349

synthetic shuttlecock under static loading at specific locations around it’s circumference. The FE model

350

was found to be in good agreement for deformations of a shuttle skirt at most load locations and could

351

recreate the overall compensatory deformation characteristics observed in experiment. However,

352

simplifications of the shuttle geometry and unknown material properties of the modelled shuttle skirt meant

353

that there were errors in measured deflections between the experiment and simulation. Further investigation

354

of shuttle modelling needs to be conducted to improve agreement with experiment, including improvements

355

to the current shuttle CAD geometry and a more comprehensive collection of shuttle material properties.

356 357

6. Practical Implications •

358 359

The experimental and initial finite-element investigation of a synthetic shuttle in the study has improved current understanding of shuttle deformation characteristics under static and dynamic loads.

•

Synthetic shuttle skirts have been found to exhibit the same compensatory deformation behavior under

360

static and dynamic loading due to their continuous circumferential nature, which differs significantly

361

from the deformation of a feather shuttle skirt and may have implications for future designs.

362 363

•

It has been shown that ANSYS Mechanical can be used to simulate the 3D deformation of a synthetic shuttle under static loading and could be used as a method for optimising shuttle design.

17



364

Acknowledgments

365

The author gratefully acknowledges the support of staff within the Centre for Sports Engineering Research

366

(CSER) throughout this project. The author would also like to thank CSER for funding this project and

367

supplying all shuttlecocks and other equipment used in testing.

368

Compliance with ethical standards

369

Participants were informed of test procedure and oral/written consent obtained. Sheffield Hallam University

370

Research Ethics Board approved this research.

371

Conflict of interest

372

None.

373 374

References

375

Alam, F., Chowdhury, H., Theppadungporn, C., & Subic, A. (2010). Measurements of aerodynamic

376 377 378 379

properties of badminton shuttlecocks. Procedia Engineering, 2(2), 2487–2492. Alam, F., Nutakom, C., & Chowdhury, H. (2015). Effect of Porosity of Badminton Shuttlecock on Aerodynamic Drag. Procedia Engineering, 112, 430–435. Arakawa, K., Mada, T., Komatsu, H., Shimizu, T., Satou, M., Takehara, K., & Etoh, G. (2006). Dynamic

380

Contact Behavior of a Golf Ball during an Oblique Impact. Experimental Mechanics, 46(6), 691–

381

697.

382

Bachmann, T., Emmerlich, J., Baumgartner, W., Schneider, J. M., & Wagner, H. (2012). Flexural

383

stiffness of feather shafts : geometry rules over material properties. The Journal of Experimental

384

Biology 215, 405–415.

385

Cooke, A., J. (1992) The aerodynamics and mechanics of shuttlecocks. Doctor of Philosophy, Department

386

of Engineering, University of Cambridge, New hall, Cambridge, 1992.

387

Cooke, A. J. (1999). Shuttlecock aerodynamics. Sports Engineering, 2(2), 85–96.

388

CSER (2017). 2D kinematic analysis [Check 2D]. Retrieved from

389

http://www.check2d.co.uk/download/default.html 18



390

Daish, C. B. (1972). The Physics of Ball Games. (English Universities Press, London) 168-178.

391

Goodwill, S. R., & Haake, S. J. (2004). Modelling of tennis ball impacts on a rigid surface. Proceedings

392

of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,

393

218(10), 1139–1153.

394 395 396 397 398

Goodwill, S. R., Kirk, R., & Haake, S. J. (2005). Experimental and finite element analysis of a tennis ball impact on a rigid surface. Sports Engineering, 8(3), 145–158. Hart, J. (2014). Simulation and understanding of the aerodynamic characteristics of a badminton shuttle. Procedia Engineering, 72(0), 768–773. Lin, C. S. H., Chua, C. K., & Yeo, J. H. (2013). Turnover stability of shuttlecocks - Transient angular

399

response and impact deformation of feather and synthetic shuttlecocks. Procedia Engineering, 60,

400

106–111.

401 402 403 404

Matweb (2017). Overview of material properties for Nylon 11. Available at: www.matweb.com. Accessed June 2017 Mehta, U.B. (1991) - Some Aspects of Uncertainty in Computational Fluid Dynamics Results - Jn. of Fluids Eng., 113, pp. 538-543

405

Nevins, D., & Smith, L. (n.d.). Methods for Modeling Solid Sports Ball Impacts, 1–7.

406

Soleimani, A. & Saadatfar, M. (2012). Effective Parameters on Hardness Behavior in Nanoindentation of

407

Nylon66/Clay Nanocomposite Using Representative Volume Element. International Journal of

408

Applied Physics and Mathematics, Vol. 2, No. 1, January 2012

409 410

Tanaka, K., Teranishi, Y., & Ujihashi, S. (2012). Finite element modelling and simulations for golf impact, 227(1), 20–30.

411

19