Dynamic Friction Coefficient Measurements: Device and Uncertainty Analysis

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MEASUREMENT UNCERTAINTY IN TRIBOLOGLICAL WEAR
RATE TESTING
Tony L. Schmitz, Jason E. Action, David L.
Burris, W. Gregory Sawyer, John C.
Ziegert Department of Mechanical and Aerospace
Engineering University of Florida Gainesville, FL
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Motivation

• Modes of failure for manufactured systems
• plastic deformation
• fracture
• fatigue
• excessive deflections
• wear
• Wear is generally the least predictable using
  current methods.
• Wear rate for material pair determined using a
  tribometer
• tribometer testing attempts to reproduce contact
  conditions
• Reported wear rates for nominally identical
  conditions vary (100).
• source unknown
• material pair dependent
• may be due to experimental apparatus and
  procedure
• Outline uncertainty analysis and compare to
  experiment.

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Wear rate calculation
Measurand defined as the ratio of the lost volume
(due to wear) to the product of the mean normal
force and total sliding distance (Archard).
where we can make the substitutions
Vs L1L2L3
d 2SN
Measured inputs ?m mass change L1 L2 L3
sample size mean normal force mi initial
mass S unidirectional sliding distance
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Wear rate uncertainty evaluation

• Uncertainty quantity used to characterize the
  dispersion of values that could reasonably be
  attributed to the measurand (ISO).
• Applied both analytical and Monte Carlo
  approaches.
• Analytical (ISO Guide to the Expression of
  Uncertainty in Measurement)
• First correct or compensate for all known
  systematic error sources.
• Residual uncertainty remains. Estimate using law
  of propagation of uncertainty.

Zero correlation assumed single measurand
different transducers.
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Wear rate uncertainty evaluation
Evaluate partial derivatives at standard
operating conditions
1? in output
Use mean input values
Define standard uncertainty in inputs
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Wear rate uncertainty evaluation

• Monte Carlo
• History is gaming tables at casinos in Monte
  Carlo (Hazelrigg)
• Use computer to generate random numbers (of
  stated distribution) that perturb the mean values
  of the input quantities
• Calculate the output quantity, K
• Repeat (50k points in our analysis)
• Caveat
• Random number generation can be tricky (seed,
  algorithm).
• Used Matlab? randn (normal) and rand (uniform)
  functions 21492 values before repeating.

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Tribometer description
Reciprocating pin-on-disk tribometer linear
sliding between sample and counterface.
Fn via pneumatic cylinder with feedback control
Reciprocating motion via stepper motor/leadscrew
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Experimental procedure

• 21 experiments completed under nominally
  identical contacting conditions
• single polytetrafluoroethylene (PTFE) rod CNC
  machined to dimensions of 6.35 mm x 6.35 mm x
  12.7 mm
• initial sample mass recorded
• 347 stainless steel counterface prepared by wet
  sanding using 600 grit sandpaper, cleaning with
  soap and water, and wiping with acetone
• 0.1 lt Ra lt 0.2 ?m verified by SWLI
• Fn 175 N (4.3 MPa contact pressure)
• 50.8 mm path length
• Approximately 90 min tests (2600 cycles)
• Compare spread in experimental wear rate to
  analytical and Monte Carlo uncertainty analyses
  for tribometer (PTFE low environment sensitivity).

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Standard uncertainties
Must determine standard uncertainties in inputs
?m, L1, L2, L3, mi, S, and .
1. ?m Standard Uncertainty masses recorded
using an Ohaus Adventurer digital scale (AR3130)
with resolution of 0.001 g and range of 310 g.
Manufacturer stated repeatability was 0.001 g.
Type B analysis let uncertainty be 5x
repeatability 0.005 g.
g
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Standard uncertainties
Must determine standard uncertainties in inputs
?m, L1, L2, L3, mi, S, and .
2. L1, L2, L3 standard uncertainty length
recorded Mitutoyo digital caliper (SC-6) with
range of 150 mm and a resolution of 0.1
mm. Manufacturer stated uncertainty was 0.2 mm
(Type B).
mm
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Standard uncertainties
Must determine standard uncertainties in inputs
?m, L1, L2, L3, mi, S, and .
3. mi standard uncertainty mass again recorded
using digital scale.
g
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Standard uncertainties
Must determine standard uncertainties in inputs
?m, L1, L2, L3, mi, S, and .
4. S standard uncertainty linear positioning
table, stepper motor, and controller were used to
produce contact reciprocating motion. Manufacturer
stated motion uncertainty was 0.041 mm. Repeated
attempts for 50.8 mm motion measured using LVDT.
Range was ? 0.295 mm. Apply uniform distribution
to this range to obtain
mm gt 0.041 mm, select larger
Must also consider counterface-sliding direction
misalignment.
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Standard uncertainties
mm
Because S is always gt dtable, result is biased.
mm
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Standard uncertainties
Must determine standard uncertainties in inputs
?m, L1, L2, L3, mi, S, and .
5. standard uncertainty Multi-axis force
transducer (AMTI MC3A-6-500) used to measure
normal force. Range is 2200 N in Y and 1100 N in
X and Z.

• Two primary uncertainty sources considered
• Force measurement and
• Cosine misalignment between force and counterface
  surface normal.

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Standard uncertainties
Oscillation between max/min values at frequency
of reciprocating motion. Bimodal normal
distribution separated into upper and lower bins.
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Standard uncertainties
The variances in the mean upper/lower bin forces
are calculated using (Bevington and Robinson)
The average normal force is
The variance is
N
For variance values
Type A, then
N
N
N
for
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Standard uncertainties
Must also treat potential misalignment between
counterface normal and force transducer
axis. Biased result from cosine error measured
normal force always less than true value.
Error
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Standard uncertainties
Compute standard uncertainty which incorporates
both normal force measurement and cosine error.
Requires best estimate of ?. Determined by
measuring the horizontal force produced from the
application of a vertical (gravity-based) normal
force. Removed manufacturer-specified cross-talk
to find misalignment.
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Standard uncertainties
Substitution gives
N
N
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Combined standard uncertainty
uc(K) computed analytically and by Monte Carlo
simulation.
Analytical result uc(K) 7.4x10-5 mm3/Nm Monte
Carlo 50k points, N 2600 cycles. Normal
distributions, except dtable. uc(K) 7.4x10-5
mm3/Nm and
5.05x10-4 mm3/Nm
21 single point wear-rate measurements for PTFE
on 347 stainless steel.
5.04x10-4 mm3/Nm ?(K) 6.0x10-5 mm3/Nm
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Combined standard uncertainty
Ranked uncertainty contributors gt90 dominated
by mass change standard uncertainty (0.001 g
resolution scale).
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Measurement improvement Interrupted K test
Mettler Toledo AX 205 scale - 0.01 mg (100x
greater) Micrometer 0.001 mm (100x greater) 28x
reduction in uc(K) via Monte Carlo
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Discussion
- Analysis only captures instrument
uncertainties. - Identical test conditions
attempted, not all variables controlled
(humidity, counterface repolished, different
samples). - Primary difficulty with friction/wear
testing is that sample is destroyed during
experiment. - No standard artifact available for
repeated measurements (Type A). - In this work,
we attempted to provide a model for instrument
uncertainty analysis so that comparisons between
different laboratories can be made.
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Conclusions

• - Uncertainty analysis for single point wear
  testing on reciprocating tribometer completed.
• Identified primary uncertainty contributors and
  replaced equipment.
• Acknowledgements
• Funding provided by NSF (CMS-0219889 and
  DMI-0238019). Any opinions, findings, and
  conclusions or recommendations expressed in this
  material are those of the authors and do not
  necessarily reflect the views of the National
  Science Foundation.
• The authors would like to acknowledge helpful
  discussions with Dr. Angela Davies, UNCC, during
  the completion of this work.

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