Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness*1
Toshiharu Enomae and Fumihiko Onabe
Paper Science Laboratory
Department of Biomaterial Sciences
Graduate School of Agricultural and Life Sciences
The University of Tokyo

ABSTRACT
What Parker Print-Surf (PPS) roughness means was discussed by comparing thetheoretical equation to that of Bekk smoothness and by determining the wavelength range
which PPS represents by the spectral analysis applied to the stylus profiles of paper. As amodel of air flow through channels between paper surface and the metal measuring head of an
air-leak type smoothness tester, the PPS model is more comprehensible than the Oken type
(Bekk) model. However, what the testers survey is fundamentally common to the two
methods. Thus, the two equations standing for the models are convertible and the conversion
equation was led to be G3 = 18.65 / 3 TB , where G3 is PPS roughness; TB Oken typesmoothness. The empirical data exhibited that the conversion equation applies to many papers
except those with different compressibility. The correlation between PPS roughness andcenterline average (Ra) at several cut-off wavelengths calculated from stylus surface profiles
showed that PPS tester presses out paper surface so that the surface shape agrees withroughness at a cut-off wavelength of 234 µm for calendered handsheets. This cut-off
wavelength gave the least sum of squared deviations from the theoretical conversion equation,
G 3 = 2.13 × Ra . Oken type smoothness was considered to survey the longer wavelengthcomponents than PPS smoothness. However, the best-fitting cut-off wavelength was greatly*1 This article is “Spectral Analysis of Paper Surface Profile (Part 3)”. この報文を「紙の表面形状のスペクトル解析（第 3 報）」とする。
1

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

dependent on the surface deformability of paper at a testing pressure in view of papermaking
history and converting processes.
1. INTRODUCTION
Parker Print-Surf (PPS) roughness is sometimes called a kind of printing roughness because
it correlates well to print quality. In recent publications overseas and also more recently inJapan, roughness of paper has been represented almost exclusively in terms of PPS roughness.
It is explained by the fact that PPS was adopted as an ISO method in 1979.
PPS tester was invented in early 1970’s in Britain to improve Bekk and Sheffieldsmoothness testers. The principle is the air-leak method commonly among those three types.
However, paper smoothness or roughness is expressed differently as time for a constantvolume of air to leak out, passing between a paper surface and a metal plate clamping thesample for Bekk and Sheffield or as a mean gap calculated from the flow rate for PPS,
respectively. PPS has additional improvements from the others regarding the clamping
pressure and contact area between paper and the measuring head, as described in thefollowing chapter.
In the present study, the theoretical differences between Oken type smoothness as analternative of Bekk and PPS roughness were elucidated in the first place. Then, the wavelength
PPS roughness corresponds to was determined based on the surface profiles by stylus
profilometry using the spectral analysis.
2. EXPERIMENTAL
2.1 Specifications of Oken type and PPS testers
Table 1 lists different specifications between PPS[1, 2] and Oken type[3, 4] testers. The
major ones are clamping pressure, shape of contacting part (land) of the measuring head withpaper and unit of the expressed result. Oken type was basically designed to follow Bekk’s
type so that every specification and measurement condition are equivalent to those of Bekk’s
type except for the shape of the contacting part. Accordingly, the smoothness was given in2

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

number of seconds and the smoothness value would be rather difficult to realize as indicating
surface geometry of paper. In PPS tester, high enough pressures of paper clamping are used
to simulate those of commercial printing practices. In the PPS mechanism, the measuring headconsists of a land only 51 µm wide, which contacts paper and contributes to make a narrow
channel across which air flow out. The width of the metering land is so small as to prevent air
from flowing through inside the paper or leaking out from the backside.
2.2 Theoretical equations
Measured values by the two methods are expressed in different ways. Therefore, theirequations must be carefully considered to compare what those values represent. Table 2
shows the individual equations. The mean gap G3 in Equation (1) for PPS seems to becorresponding to the pore radius r in Equation (2) for Oken type. So, the arrangement ofEquation (2) with regard to r and the substitution of the relationship (VB/TB)/P B = Q/∆P tounify the variables will give the following equation;
11

 8 µ (V B TB )  4  8 µ Q  4
r=

 =
 π ∆P  π PB… (2’)

Equation (2’) represents that the pore radius r of the model is proportional to the 4th root of
Q/∆P. To put it another way, r is inversely proportional to the 4th root of the number of
seconds, that is, the Oken type smoothness. On the other hand, the mean gap G3 of PPS is
proportional to an inverse of a cube root of Q/∆P. Besides, they are different in the coefficient;
8/π for Oken type and 12 for PPS. This discordance stems from different modeling ideas.
2.3 Differences in equation derivation and modeling
Between PPS roughness and Oken type smoothness, the derived equation depends on
what shape to regard a channel for air leak as. It is a slab for PPS or a bunch of circular tubes
for Oken type as shown in Figure 1. Following is how to derive Equations (1) and (2).
2.3.1 PPS model
Figure 2 shows the channel between parallel plates, a laminar flow model which the PPS
method assumes. Equation (1) for PPS is derived according to a general textbook[5]3Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

describing details of fluid behavior. The Navier-Stokes equation for the z component is ∂ 2v z ∂ 2v z ∂ 2v z  ∂p
 ∂vz
∂v z
∂v z
∂v z 
ρ
+ vx
+ vy
+ vz
+ 2 −+ ρg z = µ 2 +
 ∂t
∂x
∂y
∂z 
∂y 2
∂z  ∂z
 ∂x

… (3)

By the substitutions of the continuity equation: ∂v x / ∂x + ∂v y / ∂y + ∂v z / ∂z = 0 andconditions such as ∂vz / ∂t = 0 for steady state, v x = 0 , v y = 0 , ∂vz / ∂z = 0 ,∂ 2 v z / ∂z 2 = 0 , ∂vz / ∂x = 0 and ∂ 2 v z / ∂x 2 = 0 , Equation (3) simply becomes∂p∂ 2v= µ 2z
∂z
∂y

… (4)

because g z = 0 for the present case of a horizontal pipe.
p is a function of neither x nor y. Also, ∂p / ∂z is constant since v z is not a function of z.
Then, Equation (4) becomes an ordinary differential equation.
d 2 vzdp=µ= const
2
dy
dz

… (5)

Integrating Equation (5) twice using the conditions; dv z / ∂y = 0 at y = 0 for symmetry andv z = 0 at y = y 0 ,1 dp 2vz =y − y 02
2 µ dz

(

)

… (6)

Integrating this derivative, Equation (6), from -y0 to y0,
2 wy 03 dp wG3 3 ∆P
Q = ∫ w v z dy = −
=
3µ dz
12 µb
− y0
y0

where G3 = 2y0

and

… (7)

dp / dz = − ∆P / b as Figure 3 indicates necessary variables. This

comes to Equation (1).
2.3.2 Oken type model
A channel through which air flow out is regarded as number n of circular tubes with length land radius r (n=1 assumed in the equation) in the Oken type model. The calculation[6] can bemade also based on the Hagen-Poiseuille flow. Figure 4 illustrates air flow in a single circulartube.
Since v x and v y are zero, the continuity equation becomes ∂v z / ∂z = 0 . For steady state∂vz / ∂t = 0 . Then, the Navier-Stokes equation for the z component, Equation (3) becomes,

4Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

 ∂ 2 vz ∂ 2 vz ∂p= µ 2 +∂z∂y 2  ∂y… (8)To solve Equation (8), we can use cylindrical coordinates, givingz = z x = r cosθy = r sin θ r = + x 2 + y 2

θ = tan −1yx

Substituting these into Equation (8),1 dp
∂ 2 vz 1 ∂v z 1 ∂ 2 vz
=
+
+
µ dz
∂ r 2 r ∂ r r 2 ∂θ 2

… (9)This coordinates conversion is a basic formula of partial differentiation[6].
∂ 2 vz / ∂θ 2 = 0 stands because of symmetry and dp / dz is constant. So, Equation (9)becomes,d 2 v z 1 dv z 1 d  dv z 
1 dp= const =
+
=
r

µ dz
r d r r d r  dr 
dr2

… (10)

Using the conditions; dv z / dr = 0 at r = 0 for the first integration and v z = 0 at
r = R (tube radius), Equation (10) becomes,vz =(1 dp 2r − R24 µ dz)Volume velocity QB is obtained by integrating this equation from 0 to R and substituting
dp / dz = − ∆P / l in the following manner.

πR 4 dP π∆P R 4
QB = ∫ 2πrv zdr = −=8 µ dz8µ l
0RThis is how to lead Equation (2).
2.3.3 Relationship between Oken type smoothness and PPS roughness
The detailed derivations mentioned above showed that the two methods differ in whether
the gap between paper and the measuring head is regarded as a bunch of circular tubes or as aslab, although the principle is exactly common. In the Oken type model, radius r of pores can
indicate roughness of paper. However, r cannot be calculated from a measured smoothness
because the pore length l is also unknown. Therefore, it seems to be meaningless to bring in
two unknown variables in one equation. In contrast, in the slab model for PPS, the mean gap
G3, namely PPS roughness, is an only variable and explicitly decided. Besides, centerline
5

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

average roughness (Ra) very often calculated from surface profiles refers to the mean distancein the thickness direction from the centerline. Thus, Ra is expressed in the same unit with thatof PPS roughness, that is, µm. Eventually, The slab model as for PPS is definitive and morecomprehensible. However, no matter what model is assumed, the measurements are both
based on the Hagen-Poiseuille flow between the gap. Therefore, Oken type smoothness and
PPS roughness can be related using a conversion equation. The conversion equation can bederived this manner. The theoretical Equation (2) for Oken type comes from the following
equation[4],Q=

π ( Pc − P) R04
8µ

L0

=

πP r 48µ l… (11)

This relation was obtained from that flow rate of air from the constant pressure chamber to thepressure-measuring chamber is equal to that from the pressure-measuring chamber to theoutside. R0 and L0 are the radius and length of the tube connecting the two chambers,
respectively. PB in Equation (2) was replaced with P in Equation (11). Equation (1), by
replacing dP with P, becomesQ=

WG33 P
12µb… (1’)Q in both Equations (11) and (1’) is common so that the combination of the two equations
gives
π ( Pc − P ) R0 4
8µ

3

wG3 P
=
L0
12 µb

… (12)

where, R0, L0, w and b are 0.15 mm, 50 mm, 735 mm and 1 mm, respectively. Substitution of
those known instrument constants into Equation (12) gives a simple interchangeable
relationship,
18.65
G3 =
3 T
B

… (13)

This equation suggests that PPS roughness is proportional to an inverse of a cube root ofOken type smoothness. However, it must be noted that this relation could stand if thedeformed surface shape was exactly the same under the measuring head between the two
6

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

types of tester. Practically, the measured values from these two testers would not satisfy thisconversion equation even for the identical sheet of paper because of different conditions likeclamping pressure and contact area.
2.3.3 Centerline average roughness and the air-leak methods
Centerline average roughness (Ra) calculated from a surface profile is a value of verticaldistance. This means that Ra should be directly related to PPS roughness expressing the meangap, G3 of the slab model because those two have the same dimension. Thus, Ra should be
related to an inverse of a cube root of Oken type smoothness according to equation (13)although an inverse of a forth root of Oken type smoothness was plotted in our previous
paper[8] where a circular tube radius r of Oken type model was considered to be the mostindicative variable.
2.4 Experimental relation between Oken type and PPS
2.4.1 Sample preparation
2.4.1.1 Handsheets
Handsheets were prepared to be with various levels of roughness by calendering andbeating. The sheets were subsequently supercalendered on a laboratory scale at different
conditions regarding temperature, linear pressure and number of passes. Differently beaten
pulp was also used for another series of handsheets. The chosen revolution on PFI mill was 0,5000, 10000 and 15000 for softwood; 0, 5000, 10000 and 30000 for hardwood.
2.4.1.1 Rough handsheets
Very rough paper was purposely prepared by replicating sandpaper surfaces onto
handsheets at wet-press. Square-shaped handsheets were made of never-dried hardwood
bleached kraft pulp beaten to 5000 revolutions PFI mill. The replication was made according
to the following procedures. A sheet of water-resistant sandpaper was inserted between ahandsheet and a standard metal plate with the sand-filled side against the wireside of thehandsheet after the couch process. The sandpaper kept held there during the subsequentwet-press and the ring-restraint drying. The sandpaper had five grades of roughness, #400,
7

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

600, 800, 100 and 1500. The larger the number, the smoother the surface.
2.4.1.1 Machine-made basepaper and its coated grade
Machine-made basepaper for coating (P0) having a basis weight of 96.1 g/m2 was used.
Its coated grade (P1) was prepared by applying coating color consisting of 100 parts ofkaolin, 10 parts of SB-latex and 5 parts of starch to a coat weight of 5.8 g/m2. Then, those
two papers were supercalendered to different levels of roughness for another series of sample.
Table 3 shows the calendering conditions employed.
2.4.1.1 Commercial coated paper
Four kinds of commercial coated sheets were also used for the last series. They were lightweight coated paper, coat paper (as one of the categories of coated paper according to Japan
Industrial Standard), mat coated paper and cast coated paper.
2.4.2 Smoothness and roughness measurements
Oken type smoothness and PPS roughness were measured. Then, centerline averageroughness (Ra) was calculated from the stylus profiles and correlated to the PPS roughness.
Briefly, Ra means an mean distance from the centerline of a profile. The calculation proceduresfor Ra were detailed elsewhere[8-10]. The stylus profilometer used was SE-3 model, Kosaka
laboratory Inc., Osaka, Japan. For PPS roughness, Parker Print-Surf tester PPS 78, H. E.
Messmer ltd., Britain was used; for Oken type smoothness, Denso-Aspero Meter KY-5,
Asahi Seiko Inc., Tokyo, Japan.

3. RESULTS AND DISCUSSION
3.1 Empirical comparison between PPS and Oken typeFigures 5 and 6 show the empirical relationship between Oken type smoothness and PPS
roughness for the handsheets and for the machine-made sheets, respectively. Oken typesmoothness was plotted on an inverse of a cube root scale according to Equation (13). PPS
roughness was measured with a soft backing at a pressure of 0.98 MPa (10 kgf/cm2). This

8

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

PPS pressure was 10 times that of Oken type. The straight dotted line drawn from the origin
stands for the theoretical relation according to the conversion Equation (13). The entire viewof all the scattering data points may provide an idea that they do not correlate well. But, if
attention is paid to data points in the same series, some of them show an approximately linear
relation, namely within the individual series which are the supercalendered softwood
handsheets and supercalendered hardwood handsheets in Figure 5 and the supercalenderedmachine basepaper P0, its coated paper P1 and the commercial coated papers in Figure 6.
Besides, the rough sheets due to replication of the sandpaper surfaces (denoted by graytriangles) in Figure 5 differ to a great deal in Oken type smoothness, but do not show as muchdifference as it from sample to sample in PPS roughness. It is presumably because roughsurfaces were easily squeezed out in the PPS tester with a much larger clamping pressure thanin Oken type tester. The slopes of each series other than the beating and sandpaper replica
series were similar, but were shifted in parallel, probably because the surface compressibility
varied with filler loading, beating and coating. Generally, beating increases fibers and sheet
rigidity. In Figure 5, the remarkable effect of the rigidity increased by beating was observedwith the overbeaten samples (denoted by a, hardwood to 30000 rev. PFI mill; b, softwood to10000 rev.; and c, softwood 15000 rev.) as compared to others beaten to 5000 rev.
normally. Those data points are shifted upward the Y-axis with beating; unbeaten pulps d ande downward. Beating-induced rigidity seems to make a paper surface less compressive. PPS
is apt to be sensitive to surface compressibility because the clamping pressure is 10 times thatof Oken type. This sensitivity, which is important in practical printings, should be a reason why
people call PPS the printing roughness. Table 4 ensures this assumption. The reduction
percentage of PPS roughness from at 0.49 MPa (5 kgf/cm2) to at 1.96 MPa (20 kgf/cm2)
decreased with beating except for the most beaten sample. If the conversion Equation (13) iscorrect, it may be strange that there are some values of PPS roughness larger than the inverseof a cube root of Oken type smoothness for the identical sample. One possible reason for it is
the hardness of the backing material. According to the standardized test methods, the backing

9Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

of Oken type tester consists of a rubber sheet 4 mm thick with a Shore Durometer hardness of
28 units backed with a sponge sheet 3 mm thick (only a 4 mm thick pad of rubber with ahardness of 39 units for real Bekk[11]), while the PPS soft backing is neoprene litho blanket
with a hardness of 85 units[12]. Another possible reason is that the author waited for a reading
to be displayed stable for a longer time for Oken type, which made the sample morecompressed.
3.2 Calendering influence on paper surface profile
Before discussing relationship between PPS roughness and surface profile, here will beshown a typical influence of calendering on surface profiles observed with basepaper P0 andits coated paper P1. Table 3 lists conditions C0 to C5 under which those papers werecalendered. Figures 7 and 8 show changes in Ra as a function of cut-off wavelength for paper
P0 and P1, respectively. The smoothing effect on the paper surface by calendering can beseen clearly with Ra. The uncalendered sheets C0 had the largest values of Ra at larger valuesof cut-off wavelength both for P0 and P1. However, Ra of C0, as the cut-off wavelength
decreased below about 200 µm, relatively became smaller than some calendered sheets.
Flattening fiber surfaces by calendering seems to occur in a speckled manner and thus form
hills with a flat top and sharp edges. Sharp edges as on calendered sheets would give rise tohigher roughness at short cut-off wavelengths.
3.3 The relationship between PPS and surface profiles
The spectral analysis suggests how to relate PPS roughness to surface profiles. Surface
profiles were measured with the handsheets as well as with paper P0 and P1 as alreadyshown. It is our hypothesis that PPS roughness is supposed to correlate with Ra calculated
from surface profiles at certain cut-off wavelength depending on tester attributes such as theclamping pressure and paper properties. Theoretically, supposed that the surface of paper in atester is shaped sinusoidal as illustrated by Figure 9 , the mean gap G3 in PPS would be−11
 1 2π 3−
33
G3 = 
1
+
sin
θ
d
θ
=
2
.
5
≈ 136
.

∫
 2π 0


(

)

10

… (14)

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

and the Ra would be

1 2π
2
Ra =
sinθ dθ = = 0.64
∫
2π 0
π

… (15)

Thus, Equations (14) and (15) give the relationship,
G 3 = 2.13 × Ra

… (16)

Figure 10 shows Ra of stylus profiles at specified cut-off wavelengths as a function of PPS
roughness (S10) for all the handsheets. The dotted line represents the theoretical relation,
Equation (16). The beating series gave poor correlation between PPS roughness and Ra,
while that of the calendering series except the two uncalendered sheet plots away from theothers gave considerably good correlation. Turing to the numerical comparison, the plots ofthe calendered sheets came the closest on the theoretical relationship of Equation (16), thedotted line, at a cut-off wavelength of 234 µm. This cut-off wavelength was determined so thatthe sum of squared deviations from the theoretical relationship except for the two plots foruncalendered ones became the least. Equation (16) was derived when paper surface wasideally assumed sinusoidal. More irregular and deeper depressions on a practical paper
surface would make the coefficient of Equation (16) larger, thus reducing the best-fitting
cut-off wavelength to well less than 234 µm.
Figure 11 likewise shows Ra as a function of Oken type smoothness. The inverse root istaken on the horizontal axis to be with the same unit dimension as PPS roughness according toEquation (13). Oken type smoothness and Ra agreed best so that the plots fall the closest to
the line of the theoretical relationship at a cut-off wavelength of 410 µm. This cut-off
wavelength was longer than that between PPS and Ra. It suggests that PPS surveys thecomponents of shorter wavelengths of surface roughness than Oken type.
Table 5 summarizes the best-fitting cut-off wavelengths also for basepaper P0 and its
coated paper P1. The best-fitting cut-off wavelength for P0 was irregularly long because ofgrooves on the surface observed running in Machine direction. The stylus scanned the surface
in parallel to the grooves and assessed the roughness less than the overall level. Papermaking

11

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

history and converting processes should change surface shape of paper so that deformation
behavior in a air-leak roughness tester will be varied. Thus, best-fitting cut-off wavelength tocorrelate air-leak roughness to Ra of surface profiles is difficult to determine in general to allkinds of paper.

4. CONCLUSIONSAs a model of channels for air flow between paper surface and the metal measuring head ofa smoothness tester based on the air leak method, the PPS model is more comprehensible
than the Oken type (Bekk) model. It is because the PPS model has a single variable, the mean
gap to define the channel shape although the Oken type model has two variables, the pore
length and pore diameter; one needs to be evaluated to determine the other. However,regardless of the model, what the testers survey is fundamentally common to the two methods.
Thus, the two equations resulting from the different models are convertible and the conversion
equation was led to be G3 = 18.65 / 3 TB , where G3 and TB are PPS roughness and Oken
type smoothness. Commercial coated papers, machine-made basepaper for coating andvariously calendered handsheets followed this relationship well; handsheets made of variously
beaten pulps, very rough handsheets and machine-made basepaper for coating did not mainly
because of the compressibility which acted differently in the tester at the different clamping
pressures. The spectral analysis applied to stylus surface profiles resulted in that PPS testerpresses out paper surface under the measuring head so that the surface shape agrees withcenterline average roughness (Ra) at a cut-off wavelength of 234 µm for calenderedhandsheets. This cut-off wavelength gave the least sum of squared deviations from thetheoretical conversion equation, G 3 = 2.13 × Ra . Oken type smoothness was considered tosurvey the longer wavelength components than PPS. However, the best-fitting cut-off
wavelength was greatly dependent on the surface deformability of paper at a testing pressure
in view of papermaking history and converting processes.

12Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

This research was presented in part at the Annual Meeting of the Society of Fiber Scienceand Technology Japan (Tokyo, June, 1996).

ACKNOWLEDGMENT
The authors wish to thank Mr. Yozo Igarashi, Nippon Paper Industries for helping measure
PPS roughness.

REFERENCES
1. Parker, J. R., Tappi 54(6), 943(1971)
2. Parker, J. R., Tappi 64(12), 56(1981)
3. J. Tappi test methods No. 5m-74, section B, “Testing method forsmoothness and air permeability of paper and paperboard by air
micrometer.”
4. Yamamoto, K., Kaida, K. and Iwasaki M., Japan Tappi J. 20(2),81(1966)
5. Geankoplis C. J., “Transport Processes and Unit Operations”, p178,
Allyn and Bacon, Inc., Boston(1984)
6. Geankoplis C. J., “Transport Processes and Unit Operations”, p180,
Allyn and Bacon, Inc., Boston(1984)
7. For example, Marder, L., translated. by Takenouchi, O., Differentiation
andintegration

of

many

variables(Tahensu

nobisekibun),

Kyoritu-shuppan (1976)
8. Enomae, T., Ishida, S., Onabe, F., and Usuda, M., “Characterization of
air-leak smoothness of paper by analysis of correlation”, Sen'i Gakkaishi
48(9), 493(1992)
13

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

9. Enomae, T., Onabe, F., and Usuda, M., Japan Tappi J. 47(8),1002(1993).
10. Enomae, T. and Onabe, F., "Estimation of paper surface profile
measured by stylus profilometry" Sen'i Gakkaishi 49(7), 373(1993)
11. Tappi Test Methods, T 479 om-91, “Smoothness of paper (Bekk
method)”12. Operating and maintenance instructions for the Parker Print-Surfroughness tester, H. E. Messmer ltd., Britain

14

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

和文要旨「ベック法との比較による紙のパーカプリントサーフ粗さの特徴」

東京大学大学院農学生命科学系研究科生物材料科学専攻製紙科学研究室
江前敏晴、尾鍋史彦

パーカプリントサーフ(PPS)粗さがどのような紙の表面粗さを表しているかを考察した。PPS 粗さとベック平滑度の理論式の比較をまず行い、次に紙表面の触針式プロファイルのスペクトル解析から PPS が表している波長領域を求めた。理論式の比較から、紙表面と空気漏洩式平滑度計の金属ヘッドとの間にできる間隙を通る空気の流れのモデルとして、PPS モデルの方が王研（ ベック）式モデル
より合理的であることがわかった。しかし、両試験器が測定しようとするもの
は同一のものであるので、２つの理論式を関係づけることが可能であり、その変換式は G 3 = 18.65 / 3 TB （G3: PPS 粗さ、TB: 王研式平滑度）と導くことができた。測定データの比較では、この変換式が多くの紙について概ね成り立つが、叩解度のことなる紙など、圧縮性のことなるものについては成り立たなかった。
カレンダーがけした手抄き紙について、触針式プロファイルを様々なカットオ
フ値に設定して計算した中心線平均粗さ(Ra)と PPS 粗さとの相関を調べたとこ
ろ、紙の表面形状は PPS 試験器内で波長 234 µm に相当する粗さになるように変形することが示唆された。このカットオフ波長は、紙表面が正弦曲線であると仮定した場合の変換式 G 3 = 2.13 × Ra からの偏差の２乗和を最小にするものである。同様に王研式平滑度は波長 410 µm に相当する粗さを見ていることが示唆された。一般的には、変換式に最も近い関係が成り立つカットオフ波長は、抄紙や加工の方法などによって変化する、紙表面の変形特性に依存すると考えられる。

15

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

Table 1 Major differences between Oken type and PPS testers
Oken type

PPS

0.98
(1.0)

0.49, 0.98 or 1.96
(5, 10 or 20)

Nine concentric lands
1 mm wide each

A circular land
51 µm wide

Time when air flows out (s)Mean gap (µm)

Clamping pressure, MPa(kgf/cm2)
Shape of contact area
Measured value

Table 2 Comparison of the two theoretical equations
PPS 12 µ b QG3 =  w ∆P 

1
3

Oken type (Bekk)

TB =･･･(1)

G3 = mean gapµ = viscosity of air
b = distance through which air flows

8 µ VB lπ PB r 4･･･(2)

TB = Oken type smoothnessµ = viscosity of air
l = pore length
VB = air volume
PB = pressure dropr = pore radiusacross metering land

Q = volume of air flowing in unit timew = effective length of metering length∆P = pressure drop across metering land

16

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

Table 3

Calendering conditions for machine-made basepaper P0
and its coated paper P1
C0-

Condition
Pass, times
Temperature, °C
Nip pressure, kN/m

C1
1
30
39.2

C2
2
34
58.9

C3
1
75
58.9

C4
2
75
98.1

C5
2
75
144.2

Table 4 Compressibility of handsheets from variously beaten pulps. The
sample clamping pressure is 0.49 MPa (5 kgf/cm2) for S5 and 1.96 MPa (20kgf/cm2) for S20, respectively.
FurnishHardwood

PFI mill count,revolution
0
5000
10000
30000

Softwood

0
5000
10000
15000

PPS roughness, µm
S5
S20
8.66
6.83
6.35
5.24
6.25
5.36
6.77
5.55
8.71
7.99
9.11
9.24

7.18
7.22
8.28
8.29

change
S20-S5
%
-1.83
-21.2
-1.11
-17.5
-0.89
-14.2
-1.22
-18.0
-1.53
-0.77
-0.82
-0.95

-17.5
-9.6
-9.1
-10.2

Table 5 Best-fitting cut-off wavelengths to correlate centerline
average roughness (Ra) and air leak roughness or smoothness
Best-fitting wavelength, µm
Paper

PPS roughness

Oken type smoothness

Handsheets calendered

234

410

Basepaper P0> 4096> 4096

Coated paper P1

410

410

17

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

Parker Print-Surf (a slab)
Measuring head
Paper
Oken type (circular tubes)
Backing rubber

Fig. 1 Comparison of channel models between PPS and Oken type.

yxz
top platey0

2y0

flow in z direction

y0bottom plate
Fig. 2 Flow between two parallel plates as a model of PPS.

18

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

w: peripheral lengthw

Air flowG3bFig. 3 Schematic diagram of a channel for air leak in the
PPS model.

y

x
x
r

θ
z
flow in z direction

Fig. 4 Horizontal flow in a tube as a model of Oken type.

19

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

12

PPS roughness (S10), µm

10
b

c
d

8

e

a

6

4

Calendered Softwood
Calendered Hardwood
Beaten Softwood
Beaten Hardwood
Sandpaper-replicated Hardwood

2

0
0.0

0.2

0.4

0.6

0.8

Oken type smoothness, s -1/3
Fig.5 Relationship between PPS roughness and Oken type smoothness forhandsheets.

20

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

10

PPS(S10), µm

8

6

4

2

Basepaper P0
Coated paper P1Commercial coated paper

0
0.0

0.2

0.4

0.6

0.8

Oken type smoothness, s -1/3
Fig.6 Relationship between PPS roughness and Oken type smoothness formachine-made sheets. Hard backing used instead for coated paper P1.

21

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

10

Ｃ０
Ｃ１
Ｃ２
Ｃ３

Ra, m (log)

Ｃ４
Ｃ５
1

0.1
1000 100

50

30

20

Cut-off wavelength, µm (reciprocal)

Fig. 7 Calendering effect on centerline average roughness withdecreased cut-off wavelength for basepaper P0.

22

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

10

Ｃ０
Ｃ１
Ｃ２
Ｃ３

Ra, m (log)

Ｃ４
Ｃ５
1

0.1
1000 100

50

30

20

Cut-off wavelength, µm (reciprocal)

Fig. 8 Calendering effect on centerline average roughness withdecreased cut-off wavelength for coated paper P1.

23

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

yy=1+sinθ

0Paper surface

2π

θ
Head

Fig. 9 Schematic diagram of a gap between paper and the measuring
head when surface profile is assumed to be sinusoidal.

24

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

444096 µm

3

3

2

2

Theoretical relation
Calendered Softwood
Calendered Hardwood
Beaten Softwood
Beaten Hardwood

1

0
0

4

Ra, µm

273 µm

2

4

6

8

1

0
10

0

4

1638 µm

3

3

2

2

1

1

0

0
0

4

2

4

6

8

10

0

3

3

2

2

1

1

0

0
0

2

4

6

8

10

4

6

8

10

4

6

8

10

4

6

8

10

164 µm4

328 µm

2

2

16 µm

0

2

PPS roughness(S10), µm
Fig. 10

Relationship between centerline average roughness (Ra) and PPS roughness. The

length in individual figure represents a wavelength above which the wave component was25
cut-off in Ra calculation.

Enomae, T. and Onabe, F., “Characteristics of Parker Print-Surf roughness as compared with Bekk smoothness” , Sen'i Gakkaishi, 53(3): 86-95 (1997).

444096 µm

3

3

2

2

Theoretical relation
Calendered Softwood
Calendered Hardwood
Beaten Softwood
Beaten Hardwood

1

1

0

0
0.0

Ra, µm

4

0.2

0.4

0.6

0.0

4

1638 µm

3

3

2

2

1

1

0

0
0.0

4

273 µm

0.2

0.4

0.6

3

3

2

2

1

1

0

0
0.0

0.2

0.4

0.6

0.4

0.6

0.2

0.4

0.6

0.2

0.4

0.6

164 µm

0.0

4

328

0.2

16 µm

0.0

Oken type smoothness, s-1/3
Fig. 11 Relationship between centerline average roughness (Ra) and Oken type smoothness.
The length in individual figure represents a wavelength above which the wave component was26
cut-off in Ra calculation.