Experimental.numerical correlation of a padel racket subject to impact

(1)

EXPERIMENTAL

AL

L-

-

NUMERICAL CORRELATION

EXPERIM

OF A

MENTA

RIM

A

PADEL

LL UMERICAL CORRELATION

N

TA

A

LL

RACKET SUBJECT TO IMPACT

Motivation

Padel racket: main features

Study case: Marvel model

Material properties’ evaluation/estimation

FEM modelization

Static & impact tests

Results

Conclusions

Área de Mecánica de Medios Continuos y Teoría de Estructuras

Departamento de Ingeniería Civil, de Materiales y Fabricación

Universidad de Málaga

Outline

Adrián Antonio Molí Díaz; Carlos López Taboada

Germán Castillo López;

Felipe García Sánchez

EXPERIMENTAL-NUMERICAL CORRELATION OF A PADEL RACKET SUBJECT TO IMPACT. Molí Díaz, A.A.; López Taboada, C.; Castillo López, G.; García Sánchez, F.

2 / 30

DESIGN PARAMETERS

Impact surface

Frame

Core

Shaft

PLAYER’S SENSATIONS

Diamond

Teardrop

Round

Fuente: https://www.padelshack.com/how-to-choose-a-padel-racket/

Fuente:

https://www.webconsultas.com/ejercicio-y-deporte/material-deportivo/como-elegir-la-pala-de-padel-adecuada- 14616. Fuente:

http://www.hellopadel.org/padel/new/Jeremy-Gala-Belgian-WPT-Padel-player

Small company from Málaga

Motivation

(2)

3 / 30

DESIGN PARAMETERS

Impact surface

Frame

Core

Shaft

PLAYER’S SENSATIONS

Diamond

Teardrop

Round

Fuente:

Small company from Málaga

Motivation

Grip

4 / 30

DESIGN PARAMETERS

Impact surface

Frame

Core

Shaft

PLAYER’S SENSATIONS

Diamond

Teardrop

Round

Fuente:

Small company from Málaga

Motivation

(3)

5 / 30

Padel racket: main features

6 / 30

Padel racket: main features

Frame: stiffness

Shaft: stiffness

Vibration reduction

Grip

(4)

7 / 30

Padel racket: main features

Diamond

Teardrop

Round

Fuente:

https://www.webconsultas.com/ejercicio-y-deporte/material-deportivo/como-elegir-la-pala-de-padel-adecuada- 14616.

Sweet spot

Frame: stiffness

Shaft: stiffness

Vibration reduction

Grip

Strike surface

Balanced stiffness

(durability)

8 / 30

Study case: Marvel racket

• Balanced glass fabric:

ʹʹͲ

݃ݎ

Ȁ

݉

ଶ

.

• Twill 3K carbon fibre

ʹൈʹǣʹͲͲ

݃ݎ

Ȁ

݉

ଶ

.

• Hybrid braiding carbon/glass

ͶͲ

݉݉

ǣ͵ͻǤͺ

݃ݎ

Ȁ݉

.

• EVA foam (Ethylene-vinyl acetate).

• Multipurpose epoxy resin for manual lamination.

Type: ROUND

(5)

9 / 30

Br

aiding

Glass fiber [0/90]

₃

Foam EVA

Study case: Marvel racket

Glass fiber [0/90]

₃

Foam EVA

(Poly) Ethylene-vinyl acetate

Carbon fiber [0/90]

Glass fiber [0/90]

₃

Foam EVA

In

te

rnal

wa

ll

Braiding

Carbon fiber [0/90]

10 / 30

Br

aiding

Glass fiber [0/90]

₃

Foam EVA

Study case: Marvel racket

Glass fiber [0/90]

₃

Foam EVA

(Poly) Ethylene-vinyl acetate

Carbon fiber [0/90]

Glass fiber [0/90]

₃

Foam EVA

In

te

rnal

wa

ll

Braiding

(6)

11 / 30

Air bag

Br

aiding

Glass fiber [0/90]

₃

Foam EVA

b

bag

Study case: Marvel racket

Glass fiber [0/90]

₃

Foam EVA

(Poly) Ethylene-vinyl acetate

Carbon fiber [0/90]

Glass fiber [0/90]

₃

Foam EVA

In

te

rnal

wa

ll

Braiding

Carbon fiber [0/90]

12 / 30

Br

aiding

Glass fiber [0/90]

₃

Foam EVA

Study case: Marvel racket

Glass fiber [0/90]

₃

Foam EVA

(7)

13 / 30

Br

aiding

Glass fiber [0/90]

₃

Foam EVA

Study case: Marvel racket

Glass fiber [0/90]

₃

Foam EVA

(Poly) Ethylene-vinyl acetate

14 / 30

Material properties’ evaluation

ሶߝ ݏ

ିଵ

ܧݔ ሺܯܲܽሻ

Average

Deviation

ʹʹǤ ͳͲ

ିଷ

0,111

0,003

ͳ͵ʹǤ ͳͲ

ିଷ

0,1107

0,0004

͹ͻ

0,417

0,008

105 1,59

0,02

Core: EVA foam

Viscoelastic behavior

Cylindrical specimens

׎ ૛૞ ࢓࢓

(2) Drop test machine Instron CEAST 9350. Load cell

ʹǡʹͷ ݇ܰ

(1) Universal test machine Servosis ME-405/10. Load cell

ͳ ݇ܰ

Quasi-static

Tests (1)

Low velocity

impact test (2)

ܧݔ ሺܯܲܽሻ

(8)

15 / 30

Material properties’ evaluation

Laminates

Ply thickness

measurement

by optical microscopy

Resin

density

Fibre density

+

Weight fabric

Manufacturer’s data

Fibre volume (Ψܸ

௙

)

(Under zero voids volume

hypothesis)

D.B. Think

Composites [1]

[1] Notice d’utilisation des logiciels (MIC-MAC, GENLAM, LAMRANK, MATFIX). THINK COMPOSITES.

Micromechanics

Ply properties

16 / 30

Material properties’ evaluation

Laminates

Property

Carbon

Glass

ܧ

௫ ൌ ܧ

௬ ͵ʹǤͷ ܩܲܽ

ͳʹǤʹ ܩܲܽ

ܧ

௦ ʹǤ͸ ܩܲܽ

ͳǤͻ ܩܲܽ

ߥ

௫௬ ͲǤͲͶ

ͲǤͲͻ

ܺ ൌ ܻ

ʹͻͻ ܯܲܽ

ʹͻ͸ ܯܲܽ

ܺԢ ൌ ܻԢ

ͶͳͶ ܯܲܽ

ʹʹͺ ܯܲܽ

ܵ

͹͵ ܯܲܽ

ʹʹʹ ܯܲܽ

ܸ

௙

ʹͻ Ψ

ʹͷ Ψ

Density

ͳʹ͹Ͳ ݇݃Ȁ݉

ଷ

ͳͶ͵Ͳ ݇݃Ȁ݉

ଷ

Thickness

ͲǤ͵ͻ ݉݉

ͲǤ͵͵ ݉݉

Property

Unidirectional ply

Carbon

Glass

ܧ

௫ ͷͻǤͷ ܩܲܽ

ʹͲǤʹͷ ܩܲܽ

ܧ

௬ ͷǤ͵ ܩܲܽ

ͶǤͲͶ ܩܲܽ

ܧ

_௦

ʹǤ͸ ܩܲܽ

ͳǤͻ ܩܲܽ

ߥ

_௫௬

ͲǤʹͺ

ͲǤʹ͸

ܺ

͸ʹͳ ܯܲܽ

ͷͻͲ ܯܲܽ

ܺԢ

ͷ͸ʹ ܯܲܽ

͵ʹͺ ܯܲܽ

ܻ

ͶͲ ܯܲܽ

ͻ͵ ܯܲܽ

ܻԢ

ʹͶ͸ ܯܲܽ

͵ͷͶ ܯܲܽ

ܵ

͸ͺ ܯܲܽ

ʹͳ͸ ܯܲܽ

Density

ͳʹ͹Ͳ ݇݃Ȁ݉

ଷ

ͳͶ͵Ͳ ݇݃Ȁ݉

ଷ

Thickness

ͲǤͲͻͻ ݉݉

ͲǤͳʹͳ ݉݉

(9)

17 / 30

STATIC TESTS

Static & Dynamic (impact) tests

Load

Servosis ME-405/10

Load cell

ͳ

Load

max

:

ͷͲ

LVDTs

(1)

଴

ൌ Ͷ േͳɊ

(2)

଴

ൌ ͷ േʹǤͷɊ

18 / 30

Static & Dynamic (impact) tests

IMEMMEMMMEMMMMEMMEENTALNTALNTALNTALNTALNTAL--NUMENUMENUMENUMENUMENUMERICARICARICARICARICARICAL COL COL COL COL COL CORRELRRELRRELRRELRRELRRELATIOATIOATIOATIOATIOATION OFN OFN OFN OFN OFN OFAAAAAA PADEPADEPADEPADEPADEPADELLLLLLRACKRACKRACKRACKRACKRACKET SET SET SET SET SET SUBJEUBJEUBJEUBJEUBJEUBJECT TCT TCT TCT TCT TCT TOOOOO IOOOOOOOOO

IMPACT TESTS

CEAST 9350

Energy range:

ͲǤͷͻ െ ͳͺͲͲ

Impact speed:

ͲǤ͹͹ െ ʹͶ Ȁ

Drop height (simulated):

ͲǤͲ͵ െ ʹͻǤͶ

Drop mass:

ʹ െ ͹Ͳ

(10)

19 / 30

FEM modelization

CAD model from

mold’s manufacturer

2D

linear

elements

1. Linear elastic analysis: properties’ validation

2. Non-linear explicit dynamic: impact analysis

MSC-NASTRAN model

3D

linear

elements

19 / 30

20 / 30

Peak force @ impactor

Static tests

Ts

ai-W

u’

s f

ail

ur

e

inde

x

Ma

x. displacemen

t (1)

FEM modelization

(11)

21 / 30

Results

Displ(6) - Displ(7) (mm)

Load

(N)

Measurement points

1

2

3

4

5

6

7

1 st

_{step of test}

2 nd

_{step of test}

3 rd

_{step of test}

STATIC TESTS

22 / 30

Results

Displacements @ point 1 (mm)

Load

(N)

• Quasi-linear behavior.

• Hysteresis caused by the foam and (probably) by a

non linear behavior of the racket.

• Some dispersion between specimens.

• Dissimilar behavior between both faces of the

specimens.

STATIC TESTS

Results for the three specimens

Compatible with a

(12)

23 / 30

Results

Impact test conditions:

Mass:

ʹǡͶͳ ݇݃

Height:

Ͳǡͳ ݉

.

Acquisition frequency:

ͷͲͲ ݇ܪݖ

Acquisition time:

ͶͲ ݉ݏ

Load cell:

ʹʹ ݇ܰ ̷ ͳͲΨ

Impact velocity:

ͳǡͶʹ ݉Ȁݏ

Impact energy:

ʹǡ͵͸ ܬ

.

֜

Time (ms)

Load

(N)

ܧ

_ௗ

ݐ ൌ න

଴

௧ ܨሺݐሻ ȉ ݒ Ͳ ൅

ͳ

݉

_௜௠௣

ȉ න

_଴

௧ ܨ ݐ ݀ݐ ݀ݐ

Time (ms)

Three tests over

the same specimen

IMPACT TESTS

24 / 30

Results

IMPACT TESTS

All over the tests:

3 specimens

ൈ

2 strike surfaces

ൈ

3 test

Contact force peak

(N)

Contact time

(ms)

Dissipated energy

(% impact energy)

͵͸͸ േ ͵Ǥͺ Ψ

͵͹ േ ʹǤ͵ Ψ

Ͷͻ േ ͷ Ψ

Impact test conditions:

Mass:

ʹǡͶͳ ݇݃

Height:

Ͳǡͳ ݉

.

Acquisition frequency:

ͷͲͲ ݇ܪݖ

Acquisition time:

ͶͲ ݉ݏ

Load cell:

ʹʹ ݇ܰ ̷ ͳͲΨ

Impact velocity:

ͳǡͶʹ ݉Ȁݏ

Impact energy:

ʹǡ͵͸ ܬ

.

(13)

25 / 30

Results

Displacements (mm)

Load

(N)

Experimental results

Numerical results

CORRELATION

Static results

Experimental

stiffness

Numerical

stiffness

< 95%

Experimental

stiffness

<

76%

26 / 30

CORRELATION

Static results

Foam behavior influence

ܧ

_௙௢௔௠

ൌ ͲǤʹͶ ܯܲܽ

ܧ

௙௢௔௠

ൌ ͲǤͶͲ ܯܲܽ

Position (mm)

Displacemen

t

(mm)

_Experimental

Point

Ͷ

Point

͵

Point

ʹ

Point

ͳ

Point

ܮ

ሶࢿ ࢙

ି૚

ࡱ࢞ ሺࡹࡼࢇሻ

Average

Deviation

ʹʹǤ ͳͲ

ିଷ

0,111

0,003

ͳ͵ʹǤ ͳͲ

ିଷ

0,1107

0,0004

͹ͻ

0,417

0,008

105 1,59

0,02

(14)

27 / 30

CORRELATION

impact results

Time (ms)

Load (N)

Experimental results

Numerical results

Results

28 / 30

CORRELATION

impact results

Time (ms)

Load (N)

Experimental results

Numerical results

Results

Time (ms)

Load

(15)

29 / 30

Conclusions

A PRELIMINARY NUMERICAL MODEL

HAVE BEEN DEVELOPED

IT ALLOWS CORRELATE RACKETS’ DESIGN PARAMETERS

WITH ITS FINAL BEHAVIOR

A

FEM model

have been developed with the aim of

predict the racket’s behavior before its manufacturing.

This model can be a useful tool to

made efficient

design decisions

(materials and/or geometry).

The model have been

validate

by mean of static experiments.

ORRELLATIOATION OFN OFAAPADEPADELLRACKRACKET SET SUBJEUBJECT TCT TO IMO IMPACTPACTMolíM lílíDíDíazí A AA A ;LóLópezó T bTaboada Cbb

Force vs. time results for Marvel

FE model are

consistent with the

experimental records

obtained

for all over the tests.

Numerical force peaks and contact time

capture significantly well the observed

data which translates into a

efficient

evaluation of consumed energy

.

Set up a methodology for

estimating

materials properties

overcoming the

impossibility to obtain viable samples.

30 / 30

Still working

A deep analysis of

viscoelastic

behavior of foam

must be done.

The

number, size and distribution

of these holes will be

parame-ters to take under consideration especially in the analysis of

du-rability which would be the final step of this work.

Of course, when

holes

are introduced in de model, the

lamina-tes will lose stiffness and, consequently, the foam behavior will

gain leadership in the structural behavior of the racket.

¿

PLAYER’S SENSATIONS

NS ?

Fuente:

(16)

EXPERIMENTAL-NUMERICAL CORRELATION OF A PADEL RACKET SUBJECT TO IMPACT. Molí Díaz, A.A.; López Taboada, C.; Castillo López, G.; García Sánchez, F.NTAL-NNUMEMEMEEEEERICAEERICARICARICARICACACAALL CL CL COL COL CORRELORRELATION OF A PADEL RACKET SUBJECT TO IMPACT. Molí Díaz, A.A.; López