Friction on a Bowed Violin String

1
Friction on a Bowed Violin String

• Fayette Shaw
• May 8, 2002

2
Outline

• Objective
• Background
• Experimental Setup
• Observation Techniques
• Conclusions

3
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

4
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

5
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

6
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

7
SEM image of wear tracks
stick ? ?
? slip ?
8
Rosin

• What is rosin?
• Intermediary between bow and string
• Facilitates Helmholtz motion
• Abietic acid and impurities
• ClearTone
• Polymer which has properties which mimic rosin

9
Dynamic System
10
Laboratory Setup
string
nut
bridge
glass rod
11
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)

12
Optical image of wear track and reference mark
13
Procedure

• Measure force at terminations of string
• From these measurements, the friction force can
  be reconstructed

nut
bridge
14
Observation Techniques

• CCD Camera
• Used to obtain string deflection data
• Optical Microscopy
• Ordinary microscope camera
• Scanning Electron Microscopy (SEM)
• CMU Materials Science Department

15
SEM close up image of stick
16
Conclusions

• Able to reconstruct friction force
• Able to calculate energy deposited during slip
  region of cycle
• Able to correlate forces to wear tracks

17
Conclusions

• Applications in
• Tribology
• Acoustics
• Engineering

Yeheudi Menhuin (19161999)
18
Image Credits

• http//www.hilaryhahn.com
• http//www.pbs.org/wnet/americanmasters/database/m
  enuhin_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

19
Thanks

• Undergraduate Research Initiative
• Prof. R.T. Schumacher and Prof. S. Garoff
• Carnegie Mellon Physics Department