Friction on a Bowed Violin String

Fayette Shaw

May 8, 2002

Outline

• Objective

• Background

• Experimental Setup

• Observation Techniques

• Conclusions

Objective

• To characterize the friction force at the bowing point with the following variables– Normal force– Bow velocity– Rosin layer thickness– Contact temperature

• Current models are not adequate

Traditional Models

• Linear model– Constant friction force characterized by

coefficients µk, µs

– Ff = µk Fn

• Velocity dependent model– Functional dependence on bow velocity– Single value

Shortcomings

• Friction on a bowed string is not directly measurable

• Frictional force is cyclical• The rosin is a dynamic system

– Properties are time and temperature dependent• Softening• Viscosity

• Force is not single-valued for given velocity• Physical system is history dependent

Helmholtz Motion

• Describes ideal string with rigid terminations and no energy losses– Bow movement supplies lost energy

• Slip-stick cycle

• String acts on rosin– Wear tracks– Softening-hardening

SEM image of wear tracks

stick| |

| slip |

Rosin

• What is rosin?– Intermediary between bow and string– Facilitates Helmholtz motion– Abietic acid and impurities– ClearTone™

• Polymer which has properties which mimic rosin

Dynamic System

Laboratory Setup

glass rod

string nutbridge

Procedure

• Coat glass rod in rosin solution

• Make reference mark in rosin layer– Causes disturbance in data to correlate with

images

• Run glass rod across E string (660 Hz)

Optical image of wear track and reference mark

Procedure

• Measure force at terminations of string

• From these measurements, the friction force can be reconstructed

nut bridge

Observation Techniques

• CCD Camera– Used to obtain string deflection data

• Optical Microscopy– Ordinary microscope + camera

• Scanning Electron Microscopy (SEM)– CMU Materials Science Department

SEM close up image of stick

Conclusions

• Able to reconstruct friction force

• Able to calculate energy deposited during slip region of cycle

• Able to correlate forces to wear tracks

Conclusions

• Applications in – Tribology– Acoustics– Engineering

Yeheudi Menhuin (1916–1999)

Image Credits

• http://www.hilaryhahn.com

• http://www.pbs.org/wnet/americanmasters/database/menuhin_y.html

• http://www.centrum.is/hansi/

• http://library.thinkquest.org/27178/en/index.html

• http://www.nelson.planet.org.nz/~matthew/cbt.html

• http://www.theviolinman.co.uk/about.html

Thanks

• Undergraduate Research Initiative

• Prof. R.T. Schumacher and Prof. S. Garoff– Carnegie Mellon Physics Department