influence of mechanical and geometrical parameters … of mechanical and geometrical parameters on the static behavior of a violin bow in playing situation Fr´ed´eric Ablitzer Laboratoire

influence of mechanical and geometrical parameters

on the static behavior of a violin bow

in playing situation

Frederic Ablitzer

Laboratoire d’Acoustique de l’Universite du Maine – UMR CNRS 6613

PhD defence

Le Mans, France – December 5th, 2011

Examining committee

A. Askenfelt | KTH, Stockholm (Examiner) B. Cochelin | LMA, Marseille (Reviewer)R. Causse | IRCAM, Paris (Reviewer) J.P. Dalmont | LAUM, Le Mans (Supervisor)

A. Chaigne | ENSTA ParisTech, Palaiseau (Chairman) N. Dauchez | SUPMECA, Saint-Ouen (Supervisor)

G. Chevallier | SUPMECA, Saint-Ouen (Examiner) N. Poidevin | Bow maker, Dinan (Invited)

Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 1 / 50

Introduction

Paganini’s 24th Caprice (1819)

played by Alexander Markov


Introduction

Paganini’s 24th Caprice (1819)

played by Alexander Markov


Introduction

Evolution of the bow

Renaissance

Baroque

Classique

Moderne

c© N. Poidevin


Introduction


Renaissance

Baroque

Classique

Moderne

c© N. Poidevin

stickbaguette

lengthening of the stick


Introduction


Renaissance

Baroque

Classique

Moderne

c© N. Poidevin

headtete

stickbaguette


development of a head


Introduction


Renaissance

Baroque

Classique

Moderne

c© N. Poidevin

headtete

stickbaguette

buttonbouton

hairmeche

froghausse



mechanism to adjust hair tension


Introduction


Renaissance

Baroque

Classique

Moderne

c© N. Poidevin

headtete

stickbaguette

buttonbouton

hairmeche

froghausse



mechanism to adjust hair tension

inversion of the curvature


Introduction

The modern bow

Almost the same bow for 200 years


Introduction

The modern bow


Francois-Xavier Tourte(1747-1835)


Introduction

The modern bow



Pernambuco wood

standardized design


Introduction

The modern bow



Pernambuco wood

standardized design


Introduction

The modern bow



Pernambuco wood

standardized design

An achieved compromise


Introduction

Why study the bow?


Introduction

Why study the bow?

Little scientific studies on the bow


Introduction

Why study the bow?


Questions from bow makers about the physics behind the bowduring “Journees Facture Instrumentale et Sciences”(ITEMM, Le Mans)


Introduction

Why study the bow?



Pernambuco listed as endengered species since 2007in CITES, Appendix II


Introduction

Why study the bow?



Pernambuco listed as endengered species since 2007in CITES, Appendix II

Supply makers with dedicated characterization and simulation toolswithin the project PAFI supported by ANR (2009-2012)(“Plateforme d’Aide a la Facture Instrumentale”)


Introduction

3 points of view


Introduction

3 points of view

The player

What does he need?


Introduction

3 points of view

The player

What does he need?

The bow maker

How does he meetthe player’s demand?


Introduction

3 points of view

The player

What does he need?

The bow maker

How does he meetthe player’s demand?

The scientist

How can he helpthe maker?


Introduction

Player’s point of view

What does the player need?


Introduction



playability= allows to play a variety of bow strokes


Introduction




tonal qualities= allows to achieve a good tone


Introduction




tonal qualities= allows to achieve a good tone

aesthetics

price

...


Introduction

Bow maker’s point of view

How does the maker meet the player’s demand?


Introduction



wood

density

elasticity

damping


Introduction



wood

density

elasticity

damping

tapering

↓distribution of mass and stiffness


Introduction



wood

density

elasticity

damping

tapering

↓distribution of mass and stiffness

camber

↓adjustment of playing

and tonal qualities


Introduction


Making and adjustment mainly empirical...


Introduction


Making and adjustment mainly empirical...

...sometimes combined with a scientific approach

measuring stiffnessLucchimeter

Lutherie Tools


Introduction

Scientist’s point of view

How to characterize or model a bow?


Introduction



For the acoustician: bow = vibrating structure


Introduction




eigenmodes(modal analysis, FE model)[Bissinger 1993, Causse et al. 2001,

Pickering 2002, Ravina et al. 2008]


Introduction






admittance presented to the string[Schumacher 1975, Askenfelt 1995]


Introduction






admittance presented to the string[Schumacher 1975, Askenfelt 1995]

vibrations during playing[Askenfelt 1993]

→ may help to better understand and model the bow/string interaction

however, difficult to relate to bow maker’s adjustment and player’s perception


Introduction

Axes of investigation

static & dynamic properties


Introduction


TT



function of the bow:maintain the hair under tension

Introduction


TT




bow = prestressed structure

→ consequences on the behavior?

Introduction


TT




resist to player’s action



Introduction


TT







risk of buckling?

Introduction


TT





offer a certain compliance



risk of buckling?

Introduction


TT








risk of buckling?

Introduction


TT








risk of buckling?

how to control compliance?

Introduction


playability

tonal qualities

TT

?








risk of buckling?

how to control compliance?

Introduction

Introduction

1 Modelling

2 Experimental characterization

3 ResultsStatic behaviorStability

4 Playing tests

Conclusion


Modelling

Introduction

1 Modelling



4 Playing tests

Conclusion


Modelling

Modelling

��

bow without hair tension


Modelling

Modelling

��


Assumptions

stick = Euler-Bernoulli beam


Modelling

Modelling

��


Assumptions


stick oriented along the grain of the wood: longitudinal Young’s modulus is considered


Modelling

Modelling

��

��

T0


(i) ↓

tightened at playing tension T0

prestressed state

Assumptions




Modelling

Modelling

��

��

��

T0

T

F


(i) ↓


prestressed state

(ii) ↓

loaded by a force F on the hairplaying situation

Assumptions




Modelling

Modelling

��

��

��

T0

T

F


(i) ↓


prestressed state

(ii) ↓


Assumptions



hair has longitudinal stiffness


Modelling

Modelling

��

��

��

T0

T

F


(i) ↓


prestressed state

(ii) ↓


Assumptions




material is elastic


Modelling

Modelling

��

��

��

T0

T

F


(i) ↓ (i)


prestressed state

(ii) ↓ (ii)


Assumptions




material is elastic

(i) and (ii) are large transformations → geometric non-linear model


Modelling

Corotationnal approach: Illustration

Cantilever beam subject to end moment

M =2π E I

L

M


Modelling



M =2π E I

L

M


Modelling



M =2π E I

L

M

Local deformation (small)


Modelling



M =2π E I

L

M

Rigid body-motion (large)

Local deformation (small)


Modelling

2D model

Finite element model of the stick

2D Euler-Bernoulli beam elements,corotational formulation

external load : force T =[Tx Ty

]T

→ follower force→ amplitude depends ondisplacements

Lh

βhx

y

Tx

Ty

Rh


Modelling

2D model




]T


Lh

βhx

y

Tx

Ty

Rh

Model of the hair

equivalent single hair

compliance per unit length ch

relationship between T and playingforce Fy at relative abscissa γ

Ty = γFy

f (Tx , Fy , Lh, · · · ) = 0

T′

0 T0

γL0 L0

Rh


Modelling

2D model




]T


Lh

βhx

y

Tx

Ty

Rh

Model of the hair




Ty = γFy

f (Tx , Fy , Lh, · · · ) = 0

Lh

Fx

Fy F

Tx

Ty

T′

T

Rh


Modelling

2D model




]T


Lh

βhx

y

Tx

Ty

Rh

Model of the hair




Ty = γFy

f (Tx , Fy , Lh, · · · ) = 0

Lh

Fx

Fy F

Tx

Ty

T′

T

Rh

K(u)u = f(u)


Modelling

3D model

Why a 3D model?


Modelling

3D model

Why a 3D model?

player frequently tilts the bow→ lateral bending of the stick during playing


Modelling

3D model

Why a 3D model?


bow maker adjusts the lateral compliance of the bow(tapering, camber)


Modelling

3D model

Why a 3D model?


bow maker adjusts the lateral compliance of the bow(tapering, camber)

stick

hair

}

3D Euler-Bernoulli beam

corotationnal formulation


Experimental characterization

Introduction

1 Modelling



4 Playing tests

Conclusion



Measurement of bow shape

Method to determine the shape of the bow in a given state

Example: determination of camber






picture of the bow






picture of the bow

detect lower and upper edges along the bow






picture of the bow

detect lower and upper edges along the bow

approximate neutral curve with polynom of appropriate order



Determination of bow properties: Step 1

Procedure in 4 steps

1 Geometry





1 Geometry

Tapering

measurement with digital caliper

��

��

lateralvertical

dia

met

er(m

m)

x (mm)

0 100 200 300 400 500 600 7005

6

7

8

9





1 Geometry

Tapering

measurement with digital caliper

��

��

lateralvertical

dia

met

er(m

m)

x (mm)

0 100 200 300 400 500 600 7005

6

7

8

9

Camber

image processing





1 Geometry

2 Young’s modulus of the stick E






1 Geometry


Fz


force Fz at the tip





1 Geometry


Fz


force Fz at the tip

find E that minimizes difference betweenmeasured and simulated deformed shape

modelmeasurementFz = 0 N

y(m

m)

x (mm)

E = 26.7 GPa — Eh = 0.0 GPa — T0 = 0.0 N

0 650

0

20

comparison in the hair reference frame↓

elimination of rigid body motion

E = 26.7± 0.7 GPa (3%)





1 Geometry


Fz

3 Hair tension T0






1 Geometry


Fz

3 Hair tension T0

T0


tighten the bow





1 Geometry


Fz

3 Hair tension T0

T0


tighten the bow

find T0 that minimizes difference betweenmeasured and simulated deformed shape

modelmeasurementT0 = 0 N

y(m

m)

x (mm)

E = 26.7 GPa — Eh = 0.0 GPa — T0 = 66.7 N

0 650

0

20

T0 = 66.7± 3.9 N (6%)





1 Geometry


Fz

3 Hair tension T0

T0

4 Stiffness of the hair Eh

T0

bow under hair tension





1 Geometry


Fz

3 Hair tension T0

T0


Fz

T


force Fz at the tip





1 Geometry


Fz

3 Hair tension T0

T0


Fz

T


force Fz at the tip

find Eh that minimizes difference betweenmeasured and simulated deformed shape

modelmeasurementFz = 0 N

y(m

m)

x (mm)

E = 26.7 GPa — Eh = 7.2 GPa — T0 = 66.7 N

0 650

0

20

Eh = 7.2± 1.7 GPa (24%)



Validation: Measurement of compliance

Distribution of compliance along the bow?

→ simultaneous measurement of force anddeflection at several abscissas

u

F

γ = 0 γ = 1






u

F

γ = 0 γ = 1

linear2nd order polynommeasured data

γ = 0.5

γ = 1

defl

ecti

on

(mm

)force (N)

0 0.5 1 1.50

5

10

15

20






u

F

γ = 0 γ = 1

linear2nd order polynommeasured data

γ = 0.5

γ = 1

defl

ecti

on

(mm

)force (N)

0 0.5 1 1.50

5

10

15

20

compliance c =∂u

∂Fat F = 1 N

measurement in vertical and lateraldirections



Comparison between measured and simulated compliance

measurement - lateralmeasurement - vertical

bow B2

com

plia

nce

(mm

/N

)

relative abscissa γ

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1




simulation - verticalmeasurement - lateralmeasurement - vertical

bow B2

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1




simulation - lateralsimulation - verticalmeasurement - lateralmeasurement - vertical

bow B2

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1

Good agreement between numerical and experimental results → predictive model

[Ablitzer, Dauchez, Dalmont, submitted to Acta Acustica]


Results

Introduction

1 Modelling



4 Playing tests

Conclusion


Results Static behavior

Introduction

1 Modelling



4 Playing tests

Conclusion



Adjustment of a bow

a0

T0T0



Adjustment of a bow

a0

T0T0

Hair tension T0 vs hair-stick distance a0

hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow

(κ initial distance)

κ = 0 mm

y(m

m)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20

κ = −2 mmy

(mm

)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20

κ = −2 mmy

(mm

)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20

κ = −2 mmy

(mm

)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20

κ = −2 mmy

(mm

)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20

κ = −2 mmy

(mm

)

x (mm)0 650

0

20



Adjustment of a bow

a0

T0T0


hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

Shape of the bow


κ = 0 mm

y(m

m)

x (mm)0 650

0

20

κ = −2 mmy

(mm

)

x (mm)0 650

0

20

Adjustment of camber allows to reach another hair tension for the same distance



Compliance of the tightened bow

Vertical compliance along the bow c =∂u

∂FFz = 0 N

total

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1





∂FFz = 0 N

stickhairtotal

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1

Two contributions:

compliance of the hair

compliance of the stick





∂FFz = 0 N

stickhairtotal

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1

Two contributions:



Pitteroff’s model [Pitteroff 1995]

c =γ (1− γ) L0

T0︸︷︷︸

hair

+γ2

Kb︸︷︷︸

stick

hair length L0

hair tension T0

stiffness of the stick at the tip Kb

Kb

F





∂FFz = 0 N

Pitteroff’s modelstickhairtotal

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1

Two contributions:




c =γ (1− γ) L0

T0︸︷︷︸

hair

+γ2

Kb︸︷︷︸

stick

hair length L0

hair tension T0


Kb

F





∂FFz = 0.5 N


com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1

Two contributions:




c =γ (1− γ) L0

T0︸︷︷︸

hair

+γ2

Kb︸︷︷︸

stick

hair length L0

hair tension T0


Kb

F





∂FFz = 1.0 N


com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1

Two contributions:




c =γ (1− γ) L0

T0︸︷︷︸

hair

+γ2

Kb︸︷︷︸

stick

hair length L0

hair tension T0


Kb

F





∂FFz = 1.5 N


com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1

Two contributions:




c =γ (1− γ) L0

T0︸︷︷︸

hair

+γ2

Kb︸︷︷︸

stick

hair length L0

hair tension T0


Kb

F



Compliance of the tightened bow: Non-linearity


∂F

high forcelow force

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1

Consider compliance at low forces (0 N)and high forces (1.5 N)



Compliance of the tightened bow: Non-linearity


∂F

high forcelow force

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

γ = 0 γ = 1

Consider compliance at low forces (0 N)and high forces (1.5 N)

near the middle

→ stiffening behavior

near the tip

→ softening behavior



Compliance of the tightened bow: Effect of hair tension and camber

hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20




◦ low tension

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

• high tension

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20




◦ low tension

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

• high tension

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

◦ little camber

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

• much camber

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30




◦ low tension

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

• high tension

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

◦ little camber

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

• much camber

vert

ical

com

plia

nce

(mm

/N

)


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

Adjustment of camber strongly affects compliance

[Ablitzer, Dalmont, Dauchez, J. Acoust. Soc. Am. 123 (2012)]



Effect of bow tilt

Bow frequently tilted in playing(up to about 30◦)

F

ψ

axis of the string



Effect of bow tilt


F

ψ

axis of the string

Evolution of compliance with tilt angle ψ

F = 1 N | κ = 0 mm

0◦

com

plia

nce

(mm

/N

)relative abscissa γ

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

γ = 0 γ = 1



Effect of bow tilt


F

ψ

axis of the string


F = 1 N | κ = 0 mm

30◦

0◦

com

plia

nce

(mm

/N


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

γ = 0 γ = 1

Lateral compliance is higher than vertical compliance



Effect of bow tilt


F

ψ

axis of the string


F = 1 N | κ = −2 mm (more camber)

30◦

0◦

30◦

0◦

com

plia

nce

(mm

/N


0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

γ = 0 γ = 1

Lateral compliance is higher than vertical compliance


Results Stability

Introduction

1 Modelling



4 Playing tests

Conclusion


Results Stability

Stability of the bow

Load case

x

y

z Fz

εFy


Results Stability


Load case

x

y

z Fz

εFy

❶ without perturbation force (Fz only)

❷ with perturbation force (Fz + εFy )


Results Stability


Load case

x

y

z Fz

εFy

The bow may be unstable in two ways:

1 limit point instability(snap-through)

2 bifurcation instability(lateral buckling)

❶ without perturbation force (Fz only)

❷ with perturbation force (Fz + εFy )


Results Stability

Limit point instabilityfo

rce

Fz

(mm

)

displacements (mm)0 20 40 60 80 100 120

0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)

displacement uz (mm)0 20 40 60 80 100 120

0

20

40

60

80

100


— uz (vertical)- - uy (lateral)

Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability

Bifurcation instabilityfo

rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability


rce

Fz

(mm

)


0

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100



Results Stability

Critical buckling loadsfo

rce

Fz

(mm

)

displacements (mm)

Fc

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

hai

rte

nsi

on

T(N

)

displacement uz (mm)

Tc

0 20 40 60 80 100 1200

20

40

60

80

100

Buckling occurs

when T = Tc

critical hair tension

when Fz = Fc

critical playing force


Results Stability

Influence of hair tension

forc

eF

z(N

)

displacements (mm)0 50 100 150

0

1

2

3

4

5

Tc

hai

rte

nsi

on

T(N

)

displacement uz (mm)0 50 100 150

0

20

40

60

80

100

hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20


Results Stability

Influence of hair tension

forc

eF

z(N

)


0

1

2

3

4

5

Tc

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100

hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

same critical tension Tc

critical force Fc not very sensitive to hair tension


Results Stability

Influence of camber

forc

eF

z(N

)


0

1

2

3

4

5

Tc

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100

hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20


Results Stability

Influence of camber

forc

eF

z(N

)


0

1

2

3

4

5

Tc

hai

rte

nsi

on

T(N

)


0

20

40

60

80

100

hai

r-st

ick

dis

tance

(mm

)

hair tension T0 (N)0 10 20 30 40 50 60 70

−5

0

5

10

15

20

same critical tension Tc

increasing camber ⇒ critical force Fc decreases


Playing tests

Introduction

1 Modelling



4 Playing tests

Conclusion


Playing tests

Selection and adjustment of bows

Idea: vary only 2 parameters: camber and hair tension


Playing tests



❶ Selection of 3 bows

same properties (stiffness, mass, center of inertia...)

same aspect

high-quality bows in Pernambuco after Tourte model

×3


Playing tests





same aspect


❷ Adjustment of the bows

one bow with more camber (κ = −3 mm)

one bow with less camber (κ = 2 mm)

— camber +

— camber −

— reference

selection and adjustment by bow maker Jean-Grunberger


Playing tests





same aspect





❸ Characterization of the bows

— camber +

— camber −

— reference



Playing tests





same aspect





❸ Characterization of the bows

dis

tance

crin

-bag

uet

tea

0(m

m)

tension du crin T0 (N)0 20 40 60 80 100

−5

0

5

10

15

20

− +ref

— camber +

— camber −

— reference



Playing tests

Verbalization

Expert 1 Expert 2


Playing tests

Verbalization

Expert 1

1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes

Expert 2


Playing tests

Verbalization

Expert 1


2 Attack (consonants) (few ←→ many)timbre of transients

Expert 2


Playing tests

Verbalization

Expert 1



3 Playing at the frog (difficult ←→ easy)ease to play at the frog

4 String crossings (difficult ←→ easy)ease to make smooth string crossings

Expert 2


Playing tests

Verbalization

Expert 1





Expert 2


2 Spectrum (less rich ←→ more rich)timbre on long notes

3 Consonant (softer ←→ harder)timbre of transients

4 Reactivity (slow ←→ rapid)time necessary to produce the tone

5 Spring (little ←→ much)ability to separate notes


Playing tests

Verbalization

Expert 1





Expert 2






descriptors relative to playability and tonal qualities


Playing tests

Verbalization

Expert 1





Expert 2






descriptors relative to playability and tonal qualities

2 descriptors common to both experts: stability and attack


Playing tests

Pair-wise comparison task

For each configuration to be tested

prepare the bow

picture

play & compareagainst reference bow

evaluate


Playing tests



After the test

prepare the bow

picture

objective data subjective data


evaluate


Playing tests



After the test

prepare the bow

picture

objective data subjective data


evaluate

correlations?


Playing tests

Results

Significant correlations

Expert 1 | r = −0.83

atta

ques

(conso

nnes

)

jeu au talon−1 0 1

−1

0

1

playing at the frog | attack

(subjective – subjective)


Playing tests

Results


Expert 1 | r = −0.83

atta

ques

(conso

nnes

)


−1

0

1

Expert 2 | r = 0.91

tensi

on

T0

(N)

reactivite au geste−1 0 1

30

40

50

60

70

80



hair tension | reactivity

(objective – subjective)


Playing tests

Results


Expert 1 | r = −0.83

atta

ques

(conso

nnes

)


−1

0

1

Expert 2 | r = 0.91

tensi

on

T0

(N)


30

40

50

60

70

80

Expert 1 | r = 0.78

tensi

on

T0

(N)

attaques (consonnes)−1 0 1

30

40

50

60

70

80





hair tension | attack



Playing tests

Results


Expert 1 | r = −0.83

atta

ques

(conso

nnes

)


−1

0

1

Expert 2 | r = 0.91

tensi

on

T0

(N)


30

40

50

60

70

80

Expert 1 | r = 0.78

tensi

on

T0

(N)

attaques (consonnes)−1 0 1

30

40

50

60

70

80Expert 2 | r = 0.82

tensi

on

T0

(N)

consonne−1 0 1

30

40

50

60

70

80





hair tension | attack

(objective – subjective)→ result common to both players


Playing tests

Playing tests: Conclusions

✔ Influence of hair tension on player’s peception

reactivity

attacksր with hair tension


Playing tests



reactivity


✘ Stability

instability = trembling bow? → find relevant dynamic property


Playing tests



reactivity


✘ Stability


instability = buckling? → tests with bows of lower stiffness


Playing tests



reactivity


✘ Stability


instability = buckling? → tests with bows of lower stiffness

✔ Characterization of bows for the test

differences in bow properties

state in which the bow is played

}

are well determined


Conclusions & perspectives

Introduction

1 Modelling



4 Playing tests

Conclusion



Conclusion



Conclusion

static behavior of the bow strongly depends on prestress



Conclusion


bow played near its limit of stability



Conclusion



camber has a strong influence on

{playing hair tensioncompliancelimit of stability



Conclusion



camberր

has a strong influence on

{playing hair tension րcompliance րlimit of stability ց



Perspectives

NUMERICAL MODELS + PROCEDURE TO DETERMINE BOW PROPERTIES

predictive using affordable and easy-to-use equipment



Perspectives



Assistance to bow making

Characterization in workshop

Prediction upstream from fabrication or adjustment

Looking for alternative woods



Perspectives



Assistance to bow making

Characterization in workshop

Prediction upstream from fabrication or adjustment

Looking for alternative woods

Organology

Categorization of bows in museums

Information on bows in playing situation



Perspectives

playability

tonal qualities

TT




Perspectives

playability

tonal qualities

TT

?




Perspectives

playability

tonal qualities

TT

?



Dynamic properties

How do they affect playability?


Perspectives

playability

tonal qualities

TT

?



Dynamic properties


Perceptive studies+

Measurement of gesture


Perspectives

playability

tonal qualities

TT

?



Dynamic properties


Perceptive studies+


Dynamic properties

How do they affect the tone?


Perspectives

playability

tonal qualities

TT

?



Dynamic properties


Perceptive studies+


Dynamic properties


Influence on string motion?


Perspectives

playability

tonal qualities

TT

?


transient & spectrum


Dynamic properties


Perceptive studies+


Dynamic properties



Identify “signature” of the bow


Perspectives

playability

tonal qualities

TT

?

?


transient & spectrum


Dynamic properties


Perceptive studies+


Dynamic properties



Identify “signature” of the bow

Role of damping?


influence of mechanical and geometrical parameters

on the static behavior of a violin bow

in playing situation

Frederic Ablitzer

Laboratoire d’Acoustique de l’Universite du Maine – UMR CNRS 6613

PhD defence

Le Mans, France – December 5th, 2011

Examining committee

A. Askenfelt | KTH, Stockholm (Examiner) B. Cochelin | LMA, Marseille (Reviewer)R. Causse | IRCAM, Paris (Reviewer) J.P. Dalmont | LAUM, Le Mans (Supervisor)

A. Chaigne | ENSTA ParisTech, Palaiseau (Chairman) N. Dauchez | SUPMECA, Saint-Ouen (Supervisor)

G. Chevallier | SUPMECA, Saint-Ouen (Examiner) N. Poidevin | Bow maker, Dinan (Invited)


influence of mechanical and geometrical parameters … of mechanical and geometrical parameters on the static behavior of a violin bow in playing situation Fr´ed´eric Ablitzer Laboratoire

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