This document provides an overview of surface texture, including definitions of key terms like roughness, waviness, and lay. It discusses the importance of standard surface finish symbols and specifications in manufacturing. Specific objectives covered include identifying surface finish symbols, defining terms like roughness height and waviness width, and calculating different metrics of surface roughness including Ra, Rq, and Rt. Methods of measuring surface texture in both inches and metric units are also presented.

1. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/1
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
UNIT 4 SURFACE TEXTURE
OBJECTIVES
General Objectives: To understand the importance of surface texture in
engineering.
To understand the methods of calculating the surface
roughness.
Specific Objectives : At the end of this unit you will be able to:
Ø Identify the surface finish symbols that appear on a
drawing.
Ø Identify the surface texture terms/ definitions.
Ø Calculate the arithmetic mean value, Ra.
Ø Calculate the root-mean-square average, Rq.
Ø Calculate the maximum roughness height, Rt.
Ø Compare Ra and Rq.

2. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/2
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
INPUT
4.0 DEFINITION
Surface Texture is defined as a degree of finish conveyed to the machinist
by a system of symbols devised by a Standards Association, eg. ASA – American
Standards Association, BS – British Standards
Modern technology has demanded improved surface finishes to ensure
proper functioning and long life of machine parts. Pistons, bearings, and gears
depend to a great extent on a good surface finish for proper functioning and
therefore, require little or no break-in period. Finer finishes often require
additional operation, such as lapping or honing. The higher finishes are not
always required on parts and only result in higher production costs. To prevent
overfinishing a part, the desired finish is indicated on the shop drawing.
Information specifying the degree of finish is conveyed to the machinist by a
system of symbols devised by Standards Associations, eg. ASA American
Standards Association and BS British Standards. These symbols provide a
standard system of determining and indicating surface finish. The inch unit for
surface finish measurement is microinch (µin), while the metric unit is
micrometer (µm)

3. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/3
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
4.1. SURFACE TEXTURE TERMS AND DEFINITIONS
Lay
direction
Flaw
Waviness
height
Roughness
Height, Rt
Roughness Roughness
spacing width cutoff
Waviness
width
Surface profile Error of form Waviness Roughness
Figure 4.1. Standard terminology and symbols to describe surface finish
Regardless of the method of production, all surfaces have their own
characteristics, which are collectively referred to as surface texture, Fig. 4.1.
Certain guidelines have been established to identify surface texture in terms of
well-defined and measurable quantities (Figure 4.2)
4.1.1. Flaws
Flaws or defects, are random irregularities, such as scratches,
cracks, holes, depression, seams, tears or inclusions. These defects can be
caused during the machining or production process such as moulding,

4. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/4
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
drawing, forging, machining, eg, holes cause by air bubbles during
casting, crack and tears by forging and drawing process.
4.1.2. Lay
Lay or directionality, is the direction of the predominant surface
pattern caused by the machining process and it is usually visible to the
naked eye.
4.1.3. Roughness
Roughness is defined as closely spaced, irregular deviation on a
scale smaller than that of waviness. It is caused by the cutting tool or the
abrasive grain action and the machine feed. Roughness may be
superimposed on waviness.
4.1.3.1. Roughness height
Roughness height, Ra is the deviation to the centre line in
micro inches or micrometers.
4.1.3.2. Roughness width
Roughness Width is the distance between successive
roughness peaks parallel to the nominal surface in inches or
millimeters.

5. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/5
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
4.1.4. Waviness
Waviness is a recurrent deviation from a flat surface, much like
waves on the surface of water. It is measured and described in terms of
the surface between adjacent crests of the waves (waviness width) and
height between the crests and valleys of the waves (waviness height).
Waviness can be caused by:
a) deflection of tools, dies or the work piece
b) force or temperature sufficient to cause warping
c) uneven lubrication
d) vibration
e) any periodic mechanical or thermal variations on the system
during manufacturing operations.
4.1.5. Profile
The contour of a specified section through a surface.
4.1.6. Microinch and micrometer
The unit of measurement used to measure surface finish. The
microinch is equal to 0.000 001 inch and the micrometer equals to
0.000 001 meter.

6. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/6
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
4.2. STANDARD SYMBOLS TO DESCRIBE SURFACE TEXTURE/FINISH
0.02 – 2
6.3
1.6 0.01
Figure 4.2 A sample of a surface texture/finish designation
Symbols’ definition:
0.02 – Maximum waviness height (mm)
2 - Maximum waviness width (mm)
6.3 - Maximum roughness height (mm)
1.6 - Minimum roughness height (mm)
0.01 - Maximum roughness width (mm)
- Lay symbol (Lay perpendicular to the line
representing the surface to which the symbol is
applied)
Sometimes, the roughness number is used as a substitute for the
roughness value eg. N7 is equals to 1.6 µm, (Table. 4.1). Table 4.2 shows an
average surface roughness produced by standard machining processes.
Table 4.1. Roughness number and value
µm 50 25 12.5 6.3 3.2 1.6 0.8 0.4 0.2 0.1 0.05 0.025
Roughness
N12 N11 N10 N9 N8 N7 N6 N5 N4 N3 N2 N1
number

7. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/7
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
Table 4.2 Average surface roughness produced by standard machining
processes
PROCESS MICROINCHES MICROMETERS
Turning 100 - 250 2.5 - 6.3
Drilling 100 - 200 2.5 - 5.1
Reaming 50 - 150 1.3 - 3.8
Grinding 20 - 100 0.5 - 2.5
Honing 5 - 20 0.13 - 0.5
Lapping 1 - 10 0.025 - 0.254
4.3. SYMBOLS FOR SURFACE ROUGHNESS
The following symbols indicate the direction of the lay (Table 4.3)
Lay Interpretation Examples
Symbol
Lay parallel to the line representing the surface
= to which the symbol is applied
Lay perpendicular to the line representing the
surface to which the symbol is applied.
Lay angular and both direction to line
representing the surface to which symbol is
X applied
M Lay multidirectional

8. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/8
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
Lay Interpretation Examples
Symbol
Lay approximately circular relative to the centre
C of the surface to which the symbol is applied C
R
Lay approximately radial relative to the centre
R of the surface to which the symbol is applied
Pitted, protuberant, porous, or particulate non-
P directional lay
P
Figure 4.3. Standard lay symbols for engineering surfaces

9. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/9
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
ACTIVITY 4A
TEST YOUR UNDERSTANDING BEFORE CONTINUING TO THE
NEXT INPUT…!
4.1. Explain why present-day standards relating to surface texture are
very important to industry .
4.2. List and explain the types of defects found on surfaces.
4.3. Explain the following terms:
a) roughness
b) waviness
c) lay

10. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/10
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
FEEDBACK ON ACTIVITY 4A
4.1. The present-day standards such as American Standards
Association (ASA) and British Standards Association (BSA)
specifies the degree of finish on the drawing which is then conveyed
to the machinist. This is to prevent over finishing a component or
part and to be more cost-effective.
.
4.2. Types of defects found on surfaces are scratches, cracks, holes,
depression, seams, tears or inclusions. These defects can be caused
during the machining or production process such as moulding,
drawing, forging, machining, eg, holes in casting can be caused by
air bubbles during casting, crack and tears by forging and drawing
processes.
4.3. a) Roughness
Roughness is defined as closely spaced, irregular deviation on a
scale smaller than that of waviness. It is caused by the cutting tool
or the abrasive grain action and the machine feed. Roughness may
be superimposed on waviness.

11. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/11
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
b) Waviness
Waviness is a recurrent deviation from a flat surface, much like
waves on the surface of water. It is measured and described in
terms of the surface between adjacent crests of the waves (waviness
width) and height between the crests and valleys of the waves
(waviness height).
c) Lay
Lay or directionality, is the direction of the predominant surface
pattern caused by the machining process and it is usually visible to
the naked eye.

12. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/12
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
INPUT
4.4 SURFACE ROUGHNESS
Surface roughness is generally described in two methods: arithmetic mean
value and root-mean-square average.
4.4.1 The Arithmetic Mean Value, Ra.
Ra, formerly identified as AA for arithmetic average or CLA for
centre-line average is based on the schematic illustration of a rough
surface, which is shown in (Figure 4.4). The arithmetic mean value, Ra, is
defined as
a + b + c + d + e + f + ...
Ra = (4.4.1)
n
Where, all ordinates, a, b, c, …, are absolute values, and n is the number
of readings
4.4.2. The Root-Mean-Square Average, Rq.
Rq, formerly identified as RMS is defined as
a 2 + b 2 + c 2 + d 2 +...
Rq = (4.4.2)
n
The datum line AB in figure 4.4 is located so that the sum of the
area above the line is equal to the sum of the areas below the line. The
units generally used for surface roughness are µm (micrometer, or micron)
or µin (microinch). ( Note, 1µm = 40 µin and 1µin = 0.025 µm ).

13. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/13
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
A f g h i j k B
a b c d e
Centre line (datum line)
Figure 4.3. Coordinates used for surface – roughness using equations 4.4.1 &
4.4.2
3.4.3. Maximum Roughness Height, Rt
Maximum roughness height, Rt, is defined as the height from the
deepest trough to the highest peak. It indicates how much material has to
be removed in order to obtain a smooth surface by polishing or other
means
(h1 + h3 + h5 + h7 + h9 ) - (h2 + h4 + h6 + h8 + h10 )
Rt = x (4.4.3)
5
h1 h3 h6 h5 h7 h9
h2 h4 h8 h10
Figure 4.4. Maximum roughness height (Rt)

14. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/14
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
Where,
h1, h2…......hn - height of ordinates in mm
M - magnification
4.5. COMPARISON OF Ra AND Rq
The arithmetic mean value, Ra was adopted internationally in the mid-
1950s and is used widely in engineering practice. Equations 4.4.1 and 4.4.2
Rq
show that there is a relationship between Rq and Ra, as shown by the ratio .
Ra
The table 4.4 below gives this ratio for various surfaces:
Table 4.4 Ratio for various surfaces
Rq
Surface
Ra
Sine Curve 1.1
Machining by cutting 1.1
Grinding 1.2
Lapping and honing 1.4
In general, a surface cannot be describe by its Ra and Rq value alone,
since these values are averages. Two surfaces may have the same roughness
value but have actual topography which is very different. A few deep troughs on
an otherwise smooth surface, for example, do not affect the roughness values
significantly. However, the type of surface profile can be significant in terms of
friction, wear and fatigue characteristics of a manufactured product.
It is therefore, important to analyze the surface in great detail,
particularly for parts used in critical applications. Some 130 parameters have
been identified thus far for measuring surface roughness.

15. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/15
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
4.6 USING A SURFACE TEXTURE COMPARATOR
A more elaborate device for measuring surface finish is the surface
analyzer (prolimeter surface measuring instrument). It utilizes a recording
device to reproduce the surface irregularities on a graduated chart, providing an
ink-line record.
Although the surface indicator is the most common, other methods may be
used to measure surface finish with reasonable accuracy during machining
processes, including:
4.6.1. Comparison blocks.
Comparison blocks which are use for comparing the finish on the
work piece with the calibrated finish on a test block. Surface roughness
can be measured by comparison inspection or by direct measurement. In
comparison inspection the surface roughness can be estimated by
matching a work piece surface with blocks that display a series of
increasingly smooth surfaces, Fig. 4.5.
4.6.2. Commercial sets of standard finished specimens.
Commercial sets of standard finished specimens, which have up to
25 different surface finish samples. They consist of blocks or plates
having surface varying from the smoothest to the roughest likely to be
required.
These specimens ( Fig. 4.5. ) are used to check the finish of the
machined part against the sample finish to determine approximately the
finish produced of the part. It is often difficult to determine the finish

16. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/16
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
visually. In such cases, the surfaces may be compared by moving the tip of
your fingernail over the two surfaces.
Figure 4.4. Maximum roughness height (Rt)

17. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/17
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
ACTIVITY 4B
TEST YOUR UNDERSTANDING BEFORE CONTINUING WITH THE
NEXT INPUT…!
4.4. What do Ra, Rq and Rt stand for?
4.5. Describe how you would use the surface roughness comparator
gauge.

18. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/18
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
FEEDBACK ON ACTIVITY 4B
4.4
A f g h i j k B
a b c d e
Centre line (datum)
( i). The Arithmetic Mean Value, Ra.
The arithmetic mean value, Ra, is defined as
a + b + c + d + e + f + ...
Ra =
n
where all ordinates, a, b, c, …, are absolute values, and n is the
number of readings
( ii). The Root-Mean-Square Average, Rq.
Rq, is defined as
a 2 + b 2 + c 2 + d 2 +...
Rq =
n
The datum line AB in the figure above is located so that the sum of
the area above the line is equal to the sum of the areas below the
line. The units generally used for surface roughness are µm

19. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/19
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
(micrometer, or micron) or µin (microinch). Note, for example 1µm
= 40µin and 1µin = 0.025µm.
(iii). Maximum Roughness Height, Rt
Maximum roughness height, Rt, is defined as the height from the
deepest through to the highest peak. It indicates how much
material has to be removed in order to obtain a smooth surface by
polishing or other means
(h1 + h3 + h5 + h7 + h9 ) - (h2 + h4 + h6 + h8 + h10 )
Rt =
5
h1 h3 h6 h5 h7 h9
h2 h4 h8 h10
4.5. Comparison blocks which are use for comparing the finish on the
workpiece with the calibrated finish on a test block. Surface roughness
can be measured by comparison inspection or by direct measureement. In
comparison inspection the surface roughness can be estimated by
matching a workpiece surface with blocks that display a series of
increasingly smooth surfaces.

20. F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y
Y
er
er
ABB
ABB
y
y
bu
bu
2.0
2.0
to
to
re
re
J3103/4/20
he
he
k
k
lic
lic
SURFACE TEXTURE
C
C
w om w om
w
w
w. w.
A B B Y Y.c A B B Y Y.c
SELF-ASSESSMENT 4
1. What is meant by surface texture of a component?
a. Name three (3) method of indicating quality or texture number of a
surface.
b. State the importance of surface texture in engineering.
2. Sketch a surface profile of a machined surface. Label five (5) main parts.
3. Define the symbol on figure below.
0.03 – 1.5
3.2
0.01
1.6