Brian L. Vlcek

Georgia Southern University, Statesboro, Georgia

Robert C. Hendricks and Erwin V. Zaretsky

Glenn Research Center, Cleveland, Ohio

Predictive Failure of Cylindrical Coatings

Using Weibull Analysis

NASA/TM—2002-211381

July 2002
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Brian L. Vlcek

Georgia Southern University, Statesboro, Georgia

Robert C. Hendricks and Erwin V. Zaretsky

Glenn Research Center, Cleveland, Ohio

Predictive Failure of Cylindrical Coatings

Using Weibull Analysis

NASA/TM—2002-211381

July 2002

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

Ninth International Symposium on Transport Phenomena

and Dynamics of Rotating Machinery

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NASA/TM—2002-211381 1

Predictive Failure of Cylindrical Coatings Using Weibull Analysis

Brian L. Vlcek

Georgia Southern University

Statesboro, Georgia 30460–8045

Robert C. Hendricks and Erwin V. Zaretsky

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Summary

Rotating, coated wiping rollers used in a high-speed printing application failed primarily from

fatigue. Two coating materials were evaluated: a hard, cross-linked, plasticized polyvinyl chloride (PVC)

and a softer, plasticized PVC. A total of 447 tests was conducted with these coatings in a production

facility. The data were evaluated using Weibull analysis. The softer coating produced more than twice

the life of the harder cross-linked coating and reduced the wiper replacement rate by two-thirds, resulting

in minimum production interruption.

Introduction

Intaglio printing is used in high-quality applications where a desired texture is imparted to the

finished print product along with the ink. In this printing process, ink is applied to the entire surface

of the printing plate, although ink is ultimately desired only in the engraved valleys of the plate. The

excess ink on the flat plateaus between the engraved valleys (known in the trade as the “lands”) must be

removed before it is transferred to the printed product. The paper is then squeezed against the plate with

such force that ink is transferred from the capillary-like engraved lines, and the surface of the paper is

textured and/or deformed.

A coated cylinder is used as a wiping roller to remove the excess ink from the printing plates. The

wiper rotates and oscillates from side to side as excess ink is removed from the printing plate surface

before impressions are made. On press, the wiping roller sits in a tank of caustic solution where ink is

removed physically, by brushes and blades located in the tank, and chemically, from the wiper surface.

In an application of high-speed Intaglio printing, the surface coating of rotating cylindrical wiping

rollers fails because of fatigue and/or misuse. Microscopic and visual inspections of failed wiper surfaces

show that the primary mode of failure is fatigue. Fields of cracks 10 to 30 μm wide and 100 to 300 μm

long form on the surface of failed coatings. Figure 1 is a micrograph of a failed wiper coating surface

shown at a magnification of 100. Excess ink that has become entrapped in the fatigue cracks is transferred

to the printing plates, imprinting the fatigue crack images on the finished product. The failure criterion is

artistically driven and is based upon the appearance of the printed product. Thus, wipers are removed not

at the first appearance of fatigue cracks on the surface but at the first visual appearance of a crack image

transferred to the printed product.

Based upon the fatigue criterion, a test was conducted to determine the endurance of the roller coatings. The standard coating used was manufactured in-house by the user and was a hard, cross-linked,

plasticized polyvinyl chloride (PVC) thermoset. The candidate replacement coating was a softer plasticized PVC. The objectives of the research were to (a) determine the fatigue life of each of the coatings,

(b) determine the rate of coating replacement due to failure, and (c) minimize the impact of early failures.
NASA/TM—2002-211381 2

Statistical Method

Weibull Method

Waloddi Weibull (1939a,b, 1951) developed a method for statistically evaluating the fracture strength

of materials based upon small population sizes. He stated that the dispersion in material strength for a

group of homogeneous test specimens can be expressed by

ln ln ln 1 1

S

e

X

X = 













 ( )

β

where S is the probability of survival as a fraction (0 < S < 1), X is the stress or strength (N/m2 or psi), and

Xβ is the characteristic stress or strength (N/m2 or psi). By plotting the ordinate scale as ln ln(1/S) and

the abscissa scale as ln X, a cumulative distribution will plot as a straight line, which is called a “Weibull

plot.” Usually, the ordinate is graduated in statistical percent of specimens failed. Figure 2 is a generic

Weibull plot with some of the values of interest indicated.

The Weibull plot can be used to evaluate phenomena that result in a statistical distribution. The

tangent of the resulting plot, called the Weibull slope and designated by e or m, defines the statistical

distribution. Weibull slopes of 1, 2, and 3.57 represent exponential, Raleigh, and Gaussian (normal)

distributions, respectively. Lundberg and Palmgren (1947) were the first to use Weibull analysis to predict

the lives of rolling-element bearings.

The statistical method for plotting and evaluating data using Weibull analysis was developed by

Johnson (1951, 1964). It is assumed that a straight line is representative of the data, even though in many

cases the data loci are not linear. Using the method of least squares, a straight line is drawn through an

array of points on each plot. From this straight line, two significant lives are obtained for comparison:

these are the lives at which 10 and 50 percent of the specimens have failed and are designated L10 and

L50, respectively. The failure index given with each plot indicates the number of failed specimens of those

tested. The confidence number is a comparison of the repeatability of the test results. It is dependent upon

the number of failures in each group of specimens, the ratio of the lives being compared, and the Weibull

slope of each group. A confidence number of 90 percent indicates that 90 out of 100 times the qualitative

results would be the same if the tests were to be repeated.

Figure 1.—Fatigue cracks on surface of failed wiper roller 

 coating.

100 m
NASA/TM—2002-211381 3

From the Weibull plot, the values of e and Xβ are determined. With these values known, it is possible

to determine the failure rate for any time increment from equation (1).

Premature Failures

Wiper coatings were known to fail prematurely in production as a result of accidents such as blade

cuts rather than from fatigue. In an attempt to isolate the fatigue characteristics of both wiper materials

being evaluated, early failures were intentionally converted to suspensions (removed from press for reasons other than for a fatigue-failed surface). A life was selected at the point below which all failures were

converted to suspensions. This life was determined after finding a natural break in the data set and/or after

observing distinct differing regions in the Weibull plots. The probability of failure was determined for

this new data set and plotted on Weibull paper as a function of life. Weibull slope and the L10 and the L50

lives were again determined from the plot.

Specimen and Procedure

Materials

Two wiper coatings were evaluated in production. The P-series coating was a hard, cross-linked,

plasticized PVC thermoset. High-temperature curing and thermal-driven crosslinking resulted in a Shore

D 48 hardness. For the A-series coating, high-temperature curing resulted in a plasticized PVC surface

with a Shore D 28 hardness. Both coating materials were produced in-house by the user and were utilized

on the press to produce the backside of a printed surface.

Figure 2.—Sketch of Weibull plot where (Weibull) slope

 or tangent of line is m, Sis probability of survival of 

 36.8 percent at which X = Xor X/X= 1 (from Melis, 

 Zaretsky, and August, 1999).

1

X

In X

In In 1/S

X

S

Ssys = exp–[X/X]m

Xref

Sref

Ssys

arc tan m
NASA/TM—2002-211381 4

Test Method

The test method was driven by production printing practices. The two wiper coatings (P and A) were

evaluated on six backpresses as part of normal production usage (a backpress is a press that prints on

the backside of the product). The wiper coatings were inspected upon removal of the wipers from the

presses. To refurbish the cylindrical wipers, the coatings were removed and/or stripped, and the wipers

were recoated for future use. The wiper cores that could not be refurbished were repaired or discarded.

Three hundred and forty-three A-series coated wipers were evaluated over a 9-month period. Of

the 343 wiper surfaces, 265 were reported as failures and 78 as suspensions. Of the 104 P-series coated

wipers tested on the same 6 backpresses during the same time period, 85 failed and 19 were suspended.

The analysis of the data involves a single backpress and a group of six backpresses and is discussed

in the following section. The impact of premature failures is also investigated by intentionally suspending

failures below a certain threshold and determining the effect of material and failure distribution on

replacement rate.

Results and Discussion

Rotating, cylindrical, coated wiping rollers used in Intaglio printing failed primarily because of

fatigue or misuse. Two coating materials were evaluated in a production facility that had six printing

presses dedicated to printing the backside of a product. The standard coating used was a hard, crosslinked, plasticized PVC thermoset designated as P-series. The candidate replacement coating was a

plasticized PVC designated as A-series. A total of 104 P-series coatings and 343 A-series coatings was

tested over 9 months and was evaluated during printing production.

A Weibull analysis was performed on the results to determine which of the wiper coatings was

significantly better. The Weibull slope L10 and L50 lives were determined for each material. Confidence

levels comparing the two materials on all six backpresses were determined.

Data From a Single Backpress

These data are from only one backpress and the two materials (A and P). Of the 24 P-series coatings,

21 were failures and 3 were suspensions. Of the 56 A-series coatings, 42 were tested to failure and 14

were suspended. The results are shown in figure 3 and are summarized in table I. Of the two materials,

the A-series coating is the longer lived by a factor of 1.5 at the L10 life. The method of Johnson (1964)

was used to obtain a confidence level of 77 percent.

Figure 3.—Weibull plot of A-series and P-series wiper

 coating data from single backpress. Failure index:

 A-series, 42/56; P-series, 21/24.

103 104 105 106

Life, stress cycles

P-series

A-series

Statistical percent of

specimens failed

1

10

5

20

50

70

90

99
NASA/TM—2002-211381 5

Data From Six Backpresses

The data from the six backpresses were combined for each of the two coatings (P-series and A-Series)

tested. Of the 104 P-series coated wipers tested, 85 failed and 19 were suspended. Of the 343 A-series

coatings, 265 failed and 78 were suspended. The results of these tests are shown in figure 4 and are summarized in table II. The L10 life of the A-series coating was approximately 2.3 times that of the P-series.

The confidence number for these data was 99 percent.

TABLE I.æSUMMARY OF WEIBULL RESULTS FOR

P-SERIES AND A-SERIES COATING DATA FROM

SINGLE BACKPRESS

Wiper coating material on

single backpress

P-series A-series

Life,a stress cycles

L10 30 169 46 595

L50 86 902 199 145

Average life,b stress cycles 81 460 194 294

Weibull slope, e 1.78 1.30

Failure indexc 21/24 42/56

Confidence number,d percent 77 77 a

Lives at which 10 and 50 percent of specimens failed.

b

Total life of all specimens (including suspensions) divided by 

number of specimens (including suspensions). c

Number (numerator) of failures out of total tested (denominator).

d

Percent of time qualitative test results will be same if test is

 repeated.

TABLE II.æSUMMARY OF WEIBULL RESULTS FOR

P-SERIES AND A-SERIES COATING DATA

COMBINED FROM SIX BACKPRESSES

Wiper coating material on all

backpresses

Life,a stress cycles P-series A-series

L10 25 402 58 774

L50 102 886 194 179

Average life,b stress cycles 95 168 186 206

Weibull slope, e 1.35 1.58

Failure indexc 85/104 265/343

Confidence number,d percent 99 99 a

Lives at which 10 and 50 percent of specimens failed.

b

Total life of all specimens (including suspensions) divided by 

number of specimens (including suspensions). c

Number (numerator) of failures out of total tested (denominator).

d

Percent of time qualitative test results will be same if test is

 repeated.

Figure 4.—Weibull plot of A-series and P-series wiper

 coating data combined from six backpresses. Failure

 index: A-series, 265/343; P-series, 85/104.

103 104 105 106

Life, stress cycles

P-series

A-series

Statistical percent of

specimens failed 1.00

0.05

10.00

50.00

90.00

99.00
NASA/TM—2002-211381 6

Backpress Data Evaluation With Enforced Suspensions

As was experienced in production, early failures were exhibited in these data. To evaluate the effect

of these early failures on the life of each coating population, failures below a clear, natural break in the

data set were suspended. These early failures were assumed to result from mishandling by the operator

and not from fatigue failure. For the P-series data on all backpresses, all failures below 50 000 impressions were manually converted to suspensions. The six longest lives were also suspended, resulting in

a comparatively straight line (fig. 5). The A-series data set was suspended for values less than 90 000

impressions. The Weibull slope and reliability for these suspended results are provided in table III. The

ratio of the L10 lives was 1.6. The confidence number was 96 percent. Eliminating the early failures

from the analysis did not have a significant effect on the relative life of the coatings, which suggested

that early failures were coating related.

Figure 5.—Weibull plot of A-series and P-series wiper

 coating data combined from six backpresses with

 suspensions. Failure index: A-series, 204/343;

 P-series, 64/104.

103 104 105 106

Life, stress cycles

P-series

A-series

Statistical percent of

specimens failed

1.0

10.0

20.0

50.0

70.0

90.0

99.0

5.0

0.2

TABLE III.æSUMMARY OF WEIBULL RESULTS FOR

P-SERIES AND A-SERIES COATING COMBINED DATA

[Includes enforced suspensions from six backpresses.]

Wiper coating material on all

backpresses

Life,a stress cycles P-series A-series

L10 69 360 112 757

L50 113 390 247 548

Average life, stress cyclesb 95 168 186 206

Weibull slope, e 3.83 2.40

Failure indexc 64/104 204/343

Confidence number,d percent 96 96 a

Lives at which 10 and 50 percent of specimens failed.

b

Total life of all specimens (including suspensions) divided by 

number of specimens (including suspensions). c

Number (numerator) of failures out of total tested (denominator).

d

Percent of time qualitative test results will be same if test is

 repeated.
NASA/TM—2002-211381 7

Wiper Replacement Protocol

Herein, assume that individual presses make 8000 impressions an hour. Thus, an individual coating

receives 8000 stress cycles per hour or 64 000 stress cycles in an 8-hr shift. Using equation (1) and the

data from figure 4 and table II for the P-series coating, 31 percent of the coatings would fail before the

8-hr shift were completed. If the remaining wipers were not replaced before the next 8-hr shift, an additional 30 percent of the original coatings would fail and need to be replaced.

For the A-series coating data from figure 4 and table II, the replacement rate for an 8-hr shift was 11

percent or one-third that of the P-series coating. Over two shifts, or 16 hr, 30 percent of the total coatings

would be replaced. The replacement rate on the second 8-hr shift would be twice that of the first 8-hr

shift. It can be reasonably concluded that by replacing the P-series coating with the A-series coating

and replacing all wipers after each 8-hr shift, the failure rate of the wipers during an 8-hr shift could be

reduced by approximately two-thirds. A cost-benefit analysis would be required before making a business

decision based on these findings.

Summary of Results

Rotating, cylindrical, coated wiping rollers used in Intaglio printing failed primarily by fatigue. Two

coating materials were evaluated in a production facility that had six printing presses dedicated to printing

the backside of a product. In a 9-month period, over 400 wiper coatings were evaluated in printing production. The P-series coating was a hard, cross-linked, plasticized polyvinyl chloride (PVC) thermoset.

The candidate replacement coating was a softer, plasticized PVC designated as A-series. A total of

104 P-series coatings and 343 A-series coatings was tested. The following results were obtained:

1. The A-series coating had over twice the life of the P-series coating and a confidence level of

99 percent. During an 8-hr shift, the wiper replacement rate was reduced by approximately two-thirds.

2. A minimum failure rate of 11 percent was attained by replacing all A-series coated wipers after

each 8-hr shift, resulting in minimum production interruption.

3. The suspension of early failures in the analysis did not significantly alter the ratio of L10 lives

(life at which 10 percent of the specimens have failed). This result suggested that early failures were coating and not operator related.

References

Johnson, L.G. (1951): The Median Ranks of Sample Values in Their Population with an Application to

Certain Fatigue Studies. Industrial Mathematics, vol. 2, pp. 1–9.

Johnson, L.G. (1964): The Statistical Treatment of Fatigue Experiments. Elsevier Publishing Co.,

Amsterdam.

Lundberg, G.; and Palmgren, A. (1947): Dynamic Capacity of Rolling Bearings. Acta Polytechnica,

Mechanical Engineering Series, vol. 1, no. 3, Stockholm.

Melis, M.E.; Zaretsky, E.V.; and August, R. (1999): Probabilistic Analysis of Aircraft Gas Turbine Disk

Life and Reliability. AIAA Trans., J. Propulsion and Power, vol. 15, no. 5, pp. 658–666.

Weibull, W. (1939a): A Statistical Theory of the Strength of Materials. Ingeniors Vetanskaps AkademienHandlinger, no. 151.

Weibull, W. (1939b): The Phenomenon of Rupture in Solids. Ingeniors Vetanskaps AkademienHandlinger, no. 153.

Weibull, W. (1951): A Statistical Distribution Function of Wide Applicability. Trans. ASME, J. Applied

Mechanics, vol. 18, no. 3, pp. 293–297.
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E–13128–1

WU–274–00–SR–00

13

Predictive Failure of Cylindrical Coatings Using Weibull Analysis

Brian L. Vlcek, Robert C. Hendricks, and Erwin V. Zaretsky

Weibull; Fatigue; Coatings; Printing

Unclassified -Unlimited

Subject Category: 37 Distribution: Nonstandard

Prepared for the Ninth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery sponsored by the Pacific Center of Thermal Fluids Engineering, Honolulu, Hawaii, February 10–14, 2002. Brian L. Vlcek,

Georgia Southern University, Statesboro, Georgia 30460–8045; Robert C. Hendricks and Erwin V. Zaretsky, NASA Glenn

Research Center. Responsible person, Erwin V. Zaretsky, organization code 5900, 216–433–3241.

Rotating, coated wiping rollers used in a high-speed printing application failed primarily from fatigue. Two coating

materials were evaluated: a hard, cross-linked, plasticized polyvinyl chloride (PVC) and a softer, plasticized PVC. A total

of 447 tests was conducted with these coatings in a production facility. The data were evaluated using Weibull analysis.

The softer coating produced more than twice the life of the harder cross-linked coating and reduced the wiper replacement

rate by two-thirds, resulting in minimum production interruption.