R3

R

V=1000

×D×N

   T  e  c

   h  n

   i  c  a

   l

   I  n   f  o  r  m  a

   t   i  o  n

■ Theoretical (Geometrical) Surface Roughness

How to Obtain Surface Roughness Values

Theoretical Surface Roughness at Turning indicates the minimum

roughness value from the cutting conditions and it is shown by the

formula as follows:

■ Surface Roughness Symbol Caution

Relationship with Triangle Symbol

Indication in JIS Standard

 Arithmetical

Mean Roughness

Ra(μm)

0.0250.050.10.2

0.40.81.6

3.26.3

12.525

Max. HeightRoughness

Rz(μm)

0.10.20.40.8

1.63.26.3

12.525

50100

Ten PointsMean

Roughness

RzJIS(μm)

Note:

(Relationship

with Triangle)

3.26.3

25

50100

12.5

0.80.40.2

1.6

0.1

Note: Finishing symbol (Triangle▽and wave~) wasabolished from JIS standard from 1994 Revision.

・How to Indicate

  Example

①When Ra is 1.6μm→1.6μmRa

②When Rz is 6.3μm→6.3μmRz

③When RzJIS is 6.3μm→6.3μmRzJIS

  Rz(h)＝f 

8R(rε)

2

×103

Rz(h)：Theoretical Surface Roughness〔μm〕 ｆ：Feed Rate〔mm/rev〕 Ｒ(rε)：Corner Radius of Insert〔mm〕

The above information is based on JIS B 0601-2001.However, some symbols were revised as shown in the right table inaccordance with ISO Standard from JIS B 0601-2001 version.Ten Points Mean Roughness (Rz) was eliminated from 2001 versionbut it still remains as RzJIS reference, since it was popular in Japan.

Type

Max. HeightRoughnessTen Points

Mean Roughness Arithmetical Mean

Roughness

Ry

Rz

Ra

→

→

→

Rz

（RzJIS）

Ra

Symbol of JIS B 0601-1994

Symbol of JIS B 0601-2001

Example of Ra Indication

Note: The indications of Ra and Rz are different.

①When indicating upper limit onlyIndicatesurface roughness following the parameter symbol.

②When indicating both lower and upper limitIndicate surface roughness as (upper limit ~lower limit) following the parameter symbol.

①When indicating the upper limit only(when upper limit is 6.3μmRa)

②When indicating both lower and upper limit(when upper limit is 6.3μmRa, lower limit is 1.6μmRa)

6.31.6

6.3 Rz6.3

Rz6.3~1.6

Example of Ry, (Rz) Indication

Type Symbol

Rz

RzJIS

Ra

How to Obtain Explanation

Ry is obtained from the distance in micronmeter between the highest peak and thelowest valley in the range of sampledreference length (ℓ) to the direction of meanline of the roughness curve.

Rz is obtained from the total in micron meter of the mean value of the each distancebetween the mean line and 5 peaks (Yp)from the highest one, and the mean value of the each distance between the mean lineand the 5 valleys (Yv) from the lowest one,of the roughness curve in the range of sampled reference length “ℓ”.

Yp1,Yp2,Yp3,Yp4,Yp5:

Distance from the mean line to highest 5peaks in the range of sampled referencelength “ℓ”Yv1,Yv2,Yv3,Yv4,Yv5:

Distance from the mean line to the lowest 5valleys in the range of sampled referencelength “ℓ”

Ra is obtained from the following formula inmicron meter when the roughness curve isexpressed by y=f(x), taking X-axis to the meanline direction and Y-axis to the verticalmagnification of the roughness curve in therange of sampled reference length “ℓ”.

Rz＝Rp＋Rv

RzJIS＝（Yp1＋Yp2＋Yp3＋Yp4＋Yp5）＋（Yv1＋Yv2＋Yv3＋Yv4＋Yv5） 

5

Ra＝ ∫｛f(x)｝dx1ℓ

ℓ

0

ℓ

m   R  p

   R  y

   R  v

ℓ

m

   Y  v   5

   Y  v   5

   Y  p   1

   Y  p   2

   Y  p   3

   Y  p   4

   Y  v   4

   Y  v   1

   Y  v   3

   Y  v   2

ℓ

X

Y

   R  a

m

   T  e  n

   P  o

   i  n   t  s   M  e  a  n

   R  o  u  g

   h  n  e  s  s

   M  a  x .

   H  e

   i  g   h   t

   R  o  u  g

   h  n  e  s  s

   A  r   i   t   h  m  e   t   i  c  a   l   M  e  a  n

   R  o  u  g   h  n  e  s  s

Surface Roughness (JIS B 0601-2001)

R

（rε）

      R     z

      (      h      )

f

 

2839 2840

M

3.23.2

6.3

1.6

6.3

1.6

25

6.3 25

256.3

25

Milled

1. Positions of Auxiliary Symbols for Surface Symbol A surace roughness value, cut-o value or reerence length, machining method, grain direction, surace undulation, etc. are

indicated around the surace symbol as shown in Fig. 1 below.

Fig. 1 Positions of Auxiliary Symbols

a : Ra Value

b : Machining Method

c : Cut-O Value, Evaluation Length

c' : Reerence Length, Evaluation Length

d : Grain Direction

: Parameter other than Ra(tp:Parameter/Cut-O Level)

g : Surace Undulation(JIS B 0610)

Reference These symbols except a and are provided when they are needed.

Reference Under ISO 1302, a nish range should be indicated as e in Fig. 1.

Examples of Graphical Representation of Surface Texture

Surace Symbol

Removal o Material by Machining is required

Removal o Material is Prohibited

Upper Limit o Ra

(a) (b) (c)

Grain Direction

Upper and Lower Limits o Ra

(a) (b)

Machining Method

(a) (b)

1. Varieties of Surface Roughness IndicatorsDefnitions and presentations o arithmetic average roughness(Ra), maximum height(Ry), 10 spot average roughness(Rz), average concave to

convex distance(Sm), average distance between local peaks S and load length rate tp are given as parameters indicating the surace roughness

o an industrial product. Surace roughness is the arithmetical average o values at randomly extracted spots on the surace o an object.

[Centerline average roughness(Ra 75)is dened in the supplements to JIS B 0031 and JIS B 0601.]

Typical calculations of surface roughness

Reference Relation between Arithmetic Average Roughness(Ra)and Conventional Parameters

ca

gd

b

f

c'

de ge

 

[Technical Data]

Surface Roughness JIS B 0601(1994)Excerpts from JIS B 0031(1994)

[Technical Data]

Drawing Indications of Surface Texture  Excerpts fromJISB0031(1994)

Code Meaning Illustration

The trace let by a cutting instrument

is parallel to the projection plane in

the drawing.

Ex. Shaped Surace

The trace let by a cutting instrument

is perpendicular to the projection

plane in the drawing.

Ex. Shaped Surace(Side View)

Circular Cut, Cylindrical Cut

The pattern let by a cutting instrument

diagonally crosses the projection plane

in the drawing.

Ex.  Honed Surace

The pattern let by a cutting instrument

crosses in various directions or has no

grain direction.

Ex.  Lapped Surace, Superfnished

Surace and Surace Finished

with a Front Mill or End Mill

The pat tern le t by a cut t ing

instrument is virtually concentric

around the center o the plane in the

drawing.

  Ex.  Faced Surace

The pattern let by a cutting instrument

is virtually radial around the center o

the plane in the drawing.

 Arithmetic Average Roughness Ra

 A portion stretching over a reerence length in the direction in which the

average line extends is cut out rom the roughness curve. This portion

is presented in a new graph with the X axis extending in the same

direction as the average line and the Y axis representing the magnitude.

Ra is represented by the equation shown at right, in microns(μm).

Maximum Height Ry 

 A portion stretching over a reerence length in the direction in which

the average line extends is cut out rom the roughness curve. The gap

between the peak line and the trough line is measured in the direction in

which the magnitude axis extends, in microns(μm).

Reerence A portion without an abnormally high peak or abnormally low trough,

which may be regarded as a faw, is cut out over the reerence length.

Ten-spot Average Roughness Rz

 A portion stretching over a reerence length in the direction in which

the average line extends is cut out rom the roughness curve. The

average o the levels(Yp)o the highest peak to the th highest peak as

measured rom the average line and the average o the levels(Yp)o the

lowest trough to the th lowest trough similarly measured in the said

portion are added together. Rz is this sum, in microns(μm).

 Arithmetic Average RoughnessRa

Maximum HeightRy 

Ten-spot AverageRoughness Rz

Reference Length

of Ry(Rz)

ℓ(mm)

Conventional

Finish SymbolStandard Series Cut-off Value

c(mm) Graphical Representation of Surface Texture Standard Series

0.012 a0.025 a0.05 a0.1 a0.2 a

0.08

0.012 ~  0.2

0.05 s0.1 s0.2 s0.4 s0.8 s

0.05 z0.1 z0.2 z0.4 z0.8 z

0.080.25

0.25

0.80.8

0.4 a0.8 a1.6 a

0.4 ~  1.61.6 s3.2 s6.3 s

1.6 z3.2 z6.3 z

3.2 a6.3 a

2.5 3.2 ~  6.3 12.5 s25 s

12.5 z25 z 2.5

12.5 a25 a 8

12.5 ~  25 50 s100 s

50 z100 z

850 a

100 a50 ~  100 200 s

400 s200 z400 z

~− −

*Interrelations among the three types shown here are not precise, and are presented or convenience only.*Ra:The evaluation values o Ry and Rz are the cut-o value and the reerence length each multiplied by ve, respectively.

 Yp1, Yp2, Yp3, Yp4, Yp5 : Levels o the highest peak to the th highest peak in the

said portion with the reerence length ℓ.

 Yv1, Yv2, Yv3, Yv4, Yv5 : Levels o the lowest trough to the th lowest trough in the

said portion with the reerence length ℓ.

X0

        R      a

 Y

ℓ

m

        R      p

Ry=Rp+Rv

m

        R      v

        R      y

ℓ

m

        5

        Y      p        Y

      p

        4

        V        5

        Y

        3

        Y      p

        Y      p

        2

        Y

        V        4

        Y        V        3

        Y

        V        2

        1

        V        1

        Y

        Y      p

ℓ

Rz= Yp1 + Yp2 + Yp3 + Yp4 + Yp5 +  Yv1 + Yv2 + Yv3 + Yv4 + Yv5

5

Ra =1ℓ

( ) dx

ℓ

0

TraceLeftbya Cutting Instrument

TraceLeftbya Cutting Instrument

TraceLeftbya Cutting Instrument

 

〔Technical Data〕

Surface Roughness by Different Processing Methods〔Technical Data〕

Indications of Geometrical Tolerance on Drawings Excerpt fromJIS B 0021（1984）

Standard valuesof standard length

(mm)

0.1

−S −S

0.2

−S

0.4

−S

0.8

−S

1.6

−S

3.2

−S

6.3

−S

12.5

−S

25

−S

50

−S

100

−S

200

−S

400

0.25 0.8 2.5 8 25

Fo rging

C asting

D ie ca sting

H ot rolling

C old rolling

D raw ing

Extruding

Tum bling

Sa ndb lasting

R olling

Fa ce cutter grinding

P laning

C utter grinding

P recision bo ring

Filing

R oun d grinding

B oring

D rilling

Ream ing

Broac h grinding

Sh aving

G rinding

H on e finishing

Sup er finishing

B uffing

Pap er finishing

Lapping

Liquid ho ning

B urnishing

S urface rolling

Electric discharg e carving

 W ire cut electric spark

C hem ical polishing

Electrolytic abrasion

C a rving（S lotting）

Precision

Precision

P recision

P recision

P recision

P recision

P recision

P recision

Precision

Precision

P recision

Precision

Precision

P recision

Precision

Prec ision Fine M edium R ough

Precision Fine M edium R ough

P recision

▽▽▽▽▽▽ −▽▽▽▽Triangular indication

Maximum peak RyRmax.

Arithmetical meanroughness Ra

0.025 0.05 0.1 0.2 0.4 0.8 1.6 3.2 6.3 12.5 25 50 100

     φ

     φ

φ0.08

0.08

0.1

0.1

0.04

       t

  t

     t

 φ   t

   φ     t

0.02

0.01 A

A

φ0.01

A

A

A

40°

0.08

φ

AB

A

A

A100

A

φ0.03

φ0.01

A0.08

A− B

     φ

0.1

       6       0

B

A

     φ

Sφ

        t

φt

 α

t 

     φ

     t

   t

         t

         t

A− B

B

0.1

B

A

     φ

A

Kinds and Symbols of Geometrical Tolerances

ｔ

Formerdesignations

ofsurface

roughness

Working

method

The surface sho wn by the arrow of the leader line

shallbe contained betwee n two p arallelplanes

which are inclined at 40°w ith theoreticalexactness

to the datum plane A and w hich are

0.08m m apart from each other in the direction

of the arrow o f the lead er line.

Examples of diagrammatical indication and its interpretationKind of tolerance

Straightnesstolerance

Symbol

Flatnesstolerance

Circularitytolerance

Cylindricitytolerance

Profile toleranceof line

Definition of tolerance zone

 W here symbolφ is attached before the num ericalvalue indicating a tolerance zo ne, this tolerancezone is a zone in a cylinder of diam eter t.

The tolerance zo ne is a zone h eldbetwe en two parallel planes adistance t ap art.

The tolerance zo ne in the con sidered

plane is a zone betwee n two con centric

circles a d istanc e t apa rt.

The tolerance zon e is a zonecontained be tween two coa xialcylinde r surface s a distance t apa rt.

The tolerance zon e is a zone held

betwe en two lines enveloping circles of

diame ter t, the centers of

w hich are situated o n a theo retically

exa ct profile line .

This surface sh all be containedbetwe en tw o pa rallel planes0.08m m apart.

The circum ference in an y sectionnorm al to the axis shall be containedbetwe en two conce ntric circles0.1m m apart on the same p lane.

The considered surface shall becontained betw een two coa xialcylinde r surfaces 0 .1mm apart.

In any cross -section parallelto the projectionplane the considered profile sh allbe con tainedbetween two lines e nveloping circles of 0.04m min diam eter, the cen ters of wh ich are situated o na line hav ing the the oretically exa ct profile.

 W here a tolerance fram e is connected tothe dimension showing the diam eter ofacylinder,the a xis ofthe cylinder shallbe

contained a cylinder of0.08m m diameter.

Profile toleranceof surface

Parallelismtolerance

Perpendicularitytolerance

Angularitytolerance

 

M easuring plane

Positionaltolerance

Coaxialitytolerance

orconcentricity

tolerance

Symmetrytolerance

Circular run-outtolerance

The tolerance zone is a zone heldbetween the two surfaces e nvelopingthe sphe res of diam eter t, the ce ntersof w hich are s ituated on a theo reticallyexa ct profile surface .

The tolerance zo ne is a zone h eldbetwe en tw o parallel planes parallelto the datum plane and a d istance tapart from each o ther.

 W here symbo lφis attached before the num ericalvalue indicating the tolerance, the tolerance zoneis a zone w ithin a cylinder of diame ter tperpendicular to the datum plane.

The tolerance zon e is a zone held between

two p arallelplane s inclined at the spe cified

angle to the datum plane and a distance t

apart from each o ther.

 W here symbolφ is attached before the numericalvalue indicating the tolerance , the tolerance z oneis a zone w ithin a cylinde r of diam eter t wh oseaxis agrees w ith the datum axialstraight line.

The tolerance zon e is a zone within a circle orsphe re of diame ter t having its center at thetheoretically e xact location, he reinafter referred toas the“true location”.

The tolerance zon e is a zone held between

two p arallelplane s a d istance t apart from

each o ther and arranged sym m etrically about

the datum m edian plane.

The tolerance is a zone be tween two co ncentriccircles whos e centers agreewith the datum axialstraight line on a nym easuring plane norm alto the datum axialstraight line and wh ich are a distance t apa rtfrom each other in the radialdirection.

Total run-outtolerance

Th in alternate long a nd s hort dash line： Cen ter lineThin alternate long an d two short dashes line： Supplem entary projection plane or se ctiona l plane

Th ick alternate long and tw o sho rt das hes line：Projection of a feature to sup plem entary Projection plane or sectiona lplane

The tolerance zon e is a zone between two

coax ialcylinde rs having axes agreeing with

the datum axialstraight line a nd a d istance

t apart from each other in the radialdirection.

The co nsidered surface shallbe con tained

between two surfaces enveloping the

spheres of diameter 0.02mm , the ce nters

of which are situated on a surface having

the theo retically exac t profile.

The surface shown b y the arrow o f the leader

line shallbe contained between two planes

parallelto the datum plane A an d 0.01m m

apart from e ach other in the direction o f the

arrow o f the lead er line.

The axis of the cylinder show n bythe arrow of the lead er line s hallbe contained w ithin a cy linder o fdiam eter 0.01m m perpendicularto the datum plane A .

The p oint show n by the arrow of the leaderline sh allbe co ntained w ithin a circle of0.03m m diame ter having its center at thetrue location 60m m and 100m m apart,respe ctively,from the datum straight lineA an d from the datum straight line B.

The axis shown b y the arrow of the

leader line sh allbe co ntained w ithin

a cylinder of 0.01m m diame ter

wh ose axis agrees w ith the

datum axialstraight line A .

The m edian surface shown by the arrow of

the lead er line sh allbe contained betw een

two parallelplanes 0.08m m apart from

each other and arranged sym m etrically

about the datum m edian plane A .

The run-out in the radialdirection of the cylindersurface show n by the a rrow of the leader lineshallnot exceed 0.1mm on any m easuring planenorm alto the datum axialstraight line whe n thecylinder is rotated by one rotation about thedatum axialstraight line A-B.

The totalradialrun-out of the c ylinde r surfaceshow n by the arrow of the leader line sha llnotexceed 0.1m m at any point on the cylindersurface w hen the cylinder part is rotated ab outthe datum axialstraight line A -B w ith a relativem ovem ent in the axialdirection.

Formtolerance

Orientation

tolerance

Locationtolerance

Run-outtolerance

Lines use d in the d rawings in the co lum n o f“definition of tolerance zone” indicate the follow ing m eanings：Th ick s olid line or brok en line： FeatureTh ick alternate long and sho rt da sh line： D atumTh in s olid line or brok en lin e： Tolerance zon e

Tolerancedsurface

Truelocation

11301129