Study on Internal Stress Vibration andEdge Wear of a Cleaning Blade
Yoshiki NAKANE , Yu MUKOBAYASHI , Yoshihiro HATTORI

要旨

Abstract

電子写真プロセス内で使用される部品の一つであるク

A cleaning blade is one of the parts used in the electropho-

リーニングブレードの寿命はエッジの摩耗量が律速であ

tographic process. The life of the cleaning blade is deter-

り，エッジの摩耗については疲労摩耗が寄与することがmined by the amount of wear on its edge, and it is known that

知られている。疲労摩耗は，繰り返し応力が作用し，摩fatigue wear dominates the of edge wear. Fatigue wear pro-耗部に微小な亀裂が生じて剥離が発生する現象として知cess is known as follows; when repeated stress acts, micro

られており，線形累積損傷則が剛体の疲労破壊をよく説

cracks progress in the wear part, causing peelings. The linear

明する経験則として使われている。他方で，クリーニン

cumulative damage rule is used as an empirical rule that

グブレードを構成する粘弾性体の疲労摩耗を線形累積損

explains fatigue fracture of rigid body well. On the other hand,

傷規則に適用した研究はほとんど無い。

few studies have applied the fatigue wear of viscoelastic bod-

本研究の目的は，線形累積損傷則の基礎である S-N 曲
線がブレードの摩耗で成立することと，ブレードの摩耗
幅とΣni /Ni の間に相関関係があることを確認することとした。

ies that make up the cleaning blade to the linear cumulative
damage rules.
The purpose of this study is to confirm that the S-N curve,
which is the basis of the linear cumulative damage rule, holds

本研究では，光弾性法を適用し，光弾性高速動画からブレードのエッジ周辺に作用する内部応力を動的に解析

for blade wear, and that there is a correlation between blade
wear width and Σni /Ni.

した。応力の繰り返し回数の動的解析に使用したレイン

In this study, we applied photoelastic method and dynami-

フロー法は，繰り返し回数をカウントする一般的な方法

cally analyzed the internal stress acting around the edge of theの中でヒステリシスを考慮したカウント方法である。

blade from the photoelastic high-speed moving image. The

結果として，ブレードの S-N 曲線は，S が増加するに

rainflow method was used for the dynamic analysis of the num-

つれて N が減少する典型的な S-N 曲線の挙動を示した。

ber of stress repetitions, which is a counting method that con-またブレード摩耗幅とΣni /Ni は良好な相関関係を示し，siders hysteresis among the typical methods for counting theΣni /Ni ，つまり累積疲労損傷度が大きいほど，ブレード

number of repetitions.

摩耗幅が大きくなった。

As the results, the S-N curve of the blade showed typical S-N

本研究の結果から，短時間の光弾性高速動画を撮影し

curve behavior in which N decreased as S increased. The bladeて，ブレードの内部応力を可視化，さらに応力変動を追

wear width and Σni /Ni also showed a good correlation, and the

跡して得られたデータを分析し，Σni /Ni を算出すること

larger the Σni /Ni, that is, the cumulative fatigue damage, theで，摩耗幅を予測することが可能になったと言える。

larger the blade wear width.
By the results of this study, it can be said possible to predict
the wear width by visualizing the internal stress of the blade
from a short-time photoelastic high-speed video, analyzing
the data obtained by tracking the stress fluctuation, and calculating Σni /Ni.

＊ EP Process R & D Division 1, Image Engineering Development Center, R & D Headquarters Business Technologies

KONICA MINOLTA TECHNOLOGY REPORT VOL. 19 (2022)

51

1 Introduction

2 ModelIn the electrophotographic process, toner used as

2. 1 Photoelastic methodcolorant causes image noise when it remains on an

When an external force is applied to an elastic body

image carrier. A toner cleaning system is installed

having a transparent and uniform structure such as

and a cleaning blade, hereinafter referred to as acelluloid to generate stress in the elastic body, the‘blade’, is widely applied to the cleaning system. The

elastic body temporarily exhibits birefringence. Whenblade is composed of a viscoelastic body cut into apolarized light is incident on a photoelastic body, bire-

strip shape supported by a metal member, and is held

fringence produces a pair of plane polarized lights that

under pressure at the edge of the blade against theoscillates in the direction of the internal force and inimage carrier. While the image carrier, formed in a

the direction perpendicular to the internal force. Sincecylindrical shape, rotates to repeat imaging sequence,the pair of plane polarized lights passes through thefrictional force is generated between the image car-elastic body at different velocities, the light exitingrier and the edge of the blade, which results in wear

the photoelastic body has a phase difference δ withof the edge. As the edge wear increases, the blade

respect to the incident light. Since this δ is propor-

cleaning performance deteriorates, and image noise

tional to the principal stress difference, the photoelas-is triggered due to toner slipping through. Various

tic method is used as a method to analyze the stressstudies have been reported to reduce the blade edge

distribution in the elastic body by measuring δ.

wear and extend life of the blade. Several types of

The detailed method for measuring the internal

wear mechanisms have been proposed. Seino et al.

stress of the cleaning blade by the photoelastic

proposed wearing equations based on the fatigue

method is as described in the previous report [2].

wear model [1]. They predicted stick-slip behavior
causing fatigue wear of the edge and successfully

2. 2 Linear cumulative damage rule

examined the possibility by their experiments. At the

The linear cumulative damage rule is used as antime of Seino et al.'s research, there was no tech-empirical rule for estimating the life when the ampli-

nique to measure the stress acting on the edge of thetude and frequency of stress acting on an object areblade, so a tensile fatigue test was conducted byirregular. This method is used when external stressapplying a repetitive stress with constant amplitudeacts on a rigid body that receives repeated loads.

and frequency to the blade. They concluded induc-Fig. 1 is called a fatigue strength curve, and it is also

tively that the vibration acting on the edge caused

called a S-N curve because it takes the magnitude of

fatigue wear.

stress and the number of repetitions as axes. WhenIn our previous report, “Visualization of internal
stress of cleaning blade by photoelastic method” [2],we proposed a method to visualize the internal stressof the blade and discussed its validity as a measurement method by means of static analysis, and themagnitude of the stress. Dynamic analysis was carried over to the next report. Therefore, in this study,
we brushed up this method and dynamically ana-

the fatigue life due to constant repetitive stress ofstress σi (i = 1, 2,…, m) of arbitrary magnitude is Ni (i= 1, 2,…, m), respectively, the σi that actually acts if

the number of stress repetitions is ni , the degree of

fatigue damage due to σi is ni /Ni , and it is consideredthat fatigue fracture occurs when the cumulative
fatigue damage due to all σi exceeds 1, which can be

expressed by Equation 1 [3].

lyzed the internal stress acting around the edge of theblade from the photoelastic high-speed moving

n1

image. Since it became possible to analyze the number of repetitions in addition to the magnitude of thestress acting around the edge of the blade by dynamic

σ1
n2

stressanalysis, we tried to explain the amount of wear ofσ2

the blade by applying the linear cumulative damage

σi

rule.

ni

The purpose of this study is to confirm that the S-N
curve, which is the basis of the Minor's rule of cumulative damage, holds for blade wear, and that there isa correlation between blade wear width and Σni /Ni.

52

N2 …
Ni
cycle of count

N1

Fig. 1 Example of S-N curve.

KONICA MINOLTA TECHNOLOGY REPORT VOL. 19 (2022)

m

Σ Nn
i=1

i

i

1

(1)

method, and the range-mean method, the rainflow
method is a method for counting the number of repetitions in consideration of hysteresis. Hereinafter,

Although many studies have applied the linear

the rainflow method will be described. As shown incumulative damage rule to fatigue fracture of rigid

Fig. 2, stress is on the horizontal axis and time is on

bodies, few reports have been employed it to predictthe vertical axis. Unlike normal, the vertical axis is

the occurrence of fatigue wear in viscoelastic bodies

time, pointing downwards. The time-series wave-[4]. In this study, we tried to adopt the linear cumula-form is likened to a multiple roof structure, and thetive damage rule to predict the fatigue wear of the

behavior of rain flowing from the top of the roof isblade from the magnitude and number of repetitions

emulated. Rain flows downward from the base of theof the internal stress caused by the self-excited vibra-

roof. When it reaches the eaves of the roof, it falls

tion generated in the viscoelastic body. Firstly, we

down to the lower roof and start flowing again until

focused the difference between fatigue fracture andthe flow stops due to the conditions for stopping thefatigue wear. Equation 1 expresses the conditions underflow described later. After the flow stops, the next

which fatigue fracture occurs, but fatigue wear canflow begins.

be considered to be the repeated discontinuous occur-

There are two conditions for the falls to stop. The

rence of minute fatigue fracture at the wear-gener-

first is, for example, when the flow from point 0 falls

ated portion. On this supposition, we considered that

down from point 1, it can fall down to point 3 as it is

the larger the Σni /Ni and the larger the number of

because the starting point of the flow 2 in the next

fatigue fractures, the larger the wear width of thetensile direction is on the tension side of point 0, it

blade. Based on this hypothesis, we hypothesizedflows down as it is, but the flow stops at the point 3

Equation 2 to represent the wear width ‘Wf ’ under theand the next tensile flow starts because point 4 is on

constant ‘a’.

the compression side of the point 0. The second is,for example, the flow from the point 2 stops at pointmni
Wf = a ×
i=1 NiΣ(2)

1, because the roof is already wet with the flow thathas fallen from the point 1.

Compression

2. 3 Cycle counting method
When the number of stress repetitions is measured

4’by the cumulative linear damage rule, it is necessary
to consider the properties of the object on which thestress acts, the surrounding environment, and so on.

1/2 cycle

4

1 cycle6’ 6
8For example, when some phenomena such as stress2 1 1’

0

3 1/2 cycle
5
1 cycle1 cycle799etition rate is taken into consideration. And in theTension

1/2 cycleTimecorrosion cracking are involved, the effect of the rep-

Strain1

537case of low cycle fatigue (fatigue phenomena in which
the number of repetitions is 10 4 times or less) accom-

0 2

panied by the same phenomena, it is necessary toStrainconsider the waveform shape of stress, that is, triangular wave, rectangular wave, and the like rather
than the speed. Since the blade edge of this study isclassified as high cycle fatigue in which wear becomesremarkable after 10 4 or more repetitions, it is not

8 6 4

StressFig. 2 Relationship between distortion interval and hysteresis loop by rainflow method.

necessary to consider the repetition rate and wave-

Amplitude and frequency are determined as fol-form shape. On the other hand, since the blade islows; when the conditions for stopping the flow arecomposed of a viscoelastic body as a material, it ismet, or when the flow is not stopped and the water

desirable to use a method of counting the number offalls down toward an infinite bottom, the length inrepetitions in consideration of hysteresis [5].

the horizontal axis direction of the water flow is mea-

Among typical methods for counting the number

sured as the amplitude of the corresponding half cycleof repetitions such as the peak method, the range

wave [6]. One of the features of the rainflow method

KONICA MINOLTA TECHNOLOGY REPORT VOL. 19 (2022)53

is that it deals the waveform in half cycle units. It

10000 fps. Kinovea [7] was used as the tracking soft-means the method can count the wave even if theware, and Fig. 4 also displayed the trajectory during

hysteresis loop is not closed as can be seen from thetracking. Since this study focused on the stick-slip ofhysteresis loop corresponding to the distortion.

the blade, the data acquired by tracking is limited tothe direction in which the frictional force acts. The
obtained data were output in csv format and used for

3 Experiment

cycle counting. We used the Python rainflow module

3. 1 Experimental equipment and analysis method

for the analysis. Among the outputs obtained by theFig. 3 shows an external photograph of the friction

rainflow module, the range and count are equivalenttester manufactured for this study. It is a blade-on-

to the strain and cycle of count on the S-N curve. The

disk type friction tester that imitates the cleaning sys-

cycle of count was divided by the video recording

tem of the electrophotographic process, and can test

time to obtain the number of repetitions per unit time.

the line contact slip friction between the disc and theblade. This tester consists of the following units: adisk drive unit that rotates a disk, a blade holding
unit not shown in the photo that holds the blade andpresses it against the disk, a polarized light source
unit that polarizes the light emitted from the lightsource with a polarizing plate and transmits theblade, and an imaging unit consisting of a ‘camera’
CRYSTA PI-1P manufactured by Photoron Co., Ltd.
with a built-in 1/4 wave plate connected to a lens
holding a circularly polarizing filter at the tip to create a photoelastic image from transmitted light.
Trajectory during tracking

Disk drive unit
Imaging unit

Disk

Polarized lightsource unit

Fig. 4 An example of a photoelastic image of the edge of a blade.

Blade

Blade holding unit

Fig. 3 Photograph of the friction tester prototyped for this research.

Fig. 4 shows an example of a photoelastic image
taken by the friction tester. This is a snapshot from a
photoelastic video. Fig. 5 shows a snapshot of the
optical image taken at the same time. In the opticalimage, deformation of the edge cannot be observed,
but in the photoelastic image, the color matchinglines are lined up at narrower intervals near the edge,
which means that higher internal stress is acting. In

Fig. 5 An example of an optical image of the edge of a blade.

3. 2 Derivation of S-N curve
In order to derive the S-N curve of the blade, we

the high-speed moving image acquired by applying

first extracted the conditions under which remark-the photoelastic method, the movement of the color

able fatigue wear occurs in the blade. A blade set to thematching line, that is, the fluctuation of the internal

specified conditions was installed on the AccurioPress

stress acting near the edge of the blade was quanti-

C6100 manufactured by Konica Minolta, hereinaf-

fied using the tracking software. The high-speed

ter referred to as the ‘actual machine’, durability

video was shot for about 5 seconds at a frame rate of

was evaluated, and then the edge of the blade was

54

KONICA MINOLTA TECHNOLOGY REPORT VOL. 19 (2022)

microscopically observed. The presence or absenceof fatigue wear was confirmed. When no significant
fatigue wear occurred, the level of the pure watercontact angle on the surface of the image carrier wasSchanged and the durability was evaluated again. By
repeating above operations, the conditions underwhich fatigue wear remarkably occurs were extracted.
Next, by using the friction tester, the blade and theimage carrier were set under the conditions that

0.1

cause remarkable fatigue wear extracted in the dura-

1bility evaluation of the actual machine. Photoelastic10
N (count/sec)

100

1000

Fig. 6 S-N curve of blade.

video was captured and the magnitude of stress when
fatigue wear occurs in the blade and the number ofrepetitions were obtained by analyzing the video.

Table 1

Material

Edge
angle

Pure watercontact angle

WearΣ ni /NiA

X

etitions in each stress range.

Low
Middle
High

61.8
22.2
25.2

15.1
4.0
8.4

A

Y

Low
High

29.3
25.8

8.5
5.3

3. 3 Wear width - Σni/Ni correlation

B

X

Low
Middle

36.0
29.0

9.1
6.7

The S-N curve of the blade was derived by dividing
the magnitude of the stress thus obtained into a predetermined range and measuring the number of rep-

In order to verify the relationship between theblade wear width and Σni /Ni , it is necessary toacquire the wear width and ni data under different
conditions, excluding Ni verified in 3.2. Durability

evaluation using the actual machine was carried out
to acquire wear width data. For the acquisition of ni

On the other hand, the blade wear width shownin Fig. 7 and ∑ni /Ni showed a good correlation, andthe larger the Σni /Ni, that is, the cumulative fatigue
damage, the larger the blade wear width. This rela-data, the data obtained by tracking the photoelastic

tionship was maintained even if the pure water con-image was analyzed by the rainflow method. The

tact angle of the photoconductor, the material of theparameters whose levels were changed were the pure

blade, and the angle of the edge of the blade werewater contact angle of the photoconductor, the blade

changed.

material, and the blade edge angle, and the otherparameters were fixed and verified.

70

material: A, edge angle: X

60
50

4. 1 Resutlts of S-N curve

40

The S-N curve of the blade shown in Fig. 6 was typical S-N curve behavior in which N decreased as S
increased. In addition, there is no fatigue limit thatW f (μm)

4 Results and discussion

20
10

stress or less, fatigue fracture does not occur even if

0cumulative damage rule was agreed.

4. 2 Wear width - Σni /Ni results

As shown in Table 1, the wear width of the blade

changed when the contact angle of the photoconduc-material: B, edge angle: X

30

appears only in iron-based materials (at a certain
the number of repetitions increases), and the linear

material: A, edge angle: Y

0.1

5

10
Σ n i /N i

15

20

Fig. 7 Blade wear width - Σni /Ni.

5 Conclusion
The S-N curve derived by counting the magnitude

tor, the material of the blade, and the angle of theof the internal stress of the blade and the number

edge of the blade were changed. Since no trend canof repetitions by the rainflow method showed a typi-

be found from here, the life of the blade cannot be

cal S-N curve, and it was suggested that the linear

predicted.

cumulative damage rule holds for the blade as well.

KONICA MINOLTA TECHNOLOGY REPORT VOL. 19 (2022)

55

Furthermore, it was confirmed that a direct proportional
relationship was held between the wear of the bladeand ∑ni /Ni regardless of the conditions such as thesurface condition of the blade and the photoconductor.

Previously, we have used actual machines to study
for extending the life of blades (with many materials)
by measuring the wear width of the blade tested in
the durability evaluation (which requires evaluationtime). By utilizing the results of this study, it can besaid possible to predict the wear width by visualizing
the internal stress of the blade from a short-time
photoelastic high-speed video, analyzing the dataobtained by tracking the stress fluctuation, and calculating Σni /Ni.

This study suggests that the cumulative linear dam-age rule, a method for predicting fatigue fracture
when an external stress is applied to a rigid body,may also be applied when measuring the internal
stress of a viscoelastic body. Viscoelastic bodies suchas blades have become widely applied in other fields(for example, in the case of electrophotographic process, rubber rollers for paper transport, charging,transfer, fixing rollers, etc.), and similar verifications
will continue in the future. It is hoped that this will be
carried out and that the technology for predicting
fatigue fracture of viscoelastic bodies will advance.

References[1] K. Seino, S. Yuge, and M. Uemura, “Wear characteristics andcleaning ability of cleaning blades”, Journal of Imaging Societyof Japan, 40, pp.320-329 (2001) [in Japanese].
[2] S. Higuchi, Y. Nakane, and K. Nakano,“Visualization of internal
stress of cleaning blade by photoelastic method”, Proceedings
for the Imaging Conference JAPAN 2019, pp.59-61 (2019)[in Japanese].
[3] T. Watanabe, “Design and verification of concrete structures”,
Chapter 6, p. 13, “engineering-eye”, ITOCHU Techno-solutions
Corporation, (2011) [in Japanese],https://www.engineering-eye.com/rpt/w015_watanabe/pdf/
w015_06.pdf (December 12, 2021)[4] K. Hayakawa,“Basic concept of life evaluation”, Journal of Japan
Rubber Association, 68, pp.297-306 (1995) [in Japanese][5] K. Kojima, “Cycle counting methods forfatiguew analysis”, High
Pressure Institute of Japan, 56, pp.184-188 (2018) [in Japanese][6] T. Endo, M. Matsuishi, K. Mitsunaga, K. Kobayashi, K. Takahashi“Proposal of Rain Flow Method and its application”,
Kyushu Institute of Technology Research Report Institute,28, pp.33-62 (1974) [in Japanese][7] https://www.kinovea.org/ (August 12, 2021)

Acknowledgment

Reprinted with permission of the Imaging Society of Japan, therepresentative host society of ICAI 2021, the International
Conference on Advanced Imaging 2021. The copyright of thisarticle is owned by the Imaging Society of Japan.

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KONICA MINOLTA TECHNOLOGY REPORT VOL. 19 (2022)