Definition of surface roughness
It is quantified by the deviation between the direction of the normal vector of the real surface and its ideal form.
It is understood that the machined surface has small spacing and small unevenness of peaks and valleys.
The distance (wave distance) between two wave peaks or two wave valleys is very small (below 1mm), which belongs to micro geometric error.
If these deviations are large, the surface is rough;
If they are small, the surface is smooth.
Theoretical (geometric) surface roughness.
How to obtain the surface roughness value?
The theoretical surface roughness during turning represents the roughness value under the minimum cutting condition.
The formula is as follows:
In the above formula:
Rz_{h}: theoretical surface roughness, unit: µ m.
f: Feed per revolution, in mm / rev.
The feed rate is calculated as follows:
In the above formula
L is the cutting length per minute, in mm / min.
N is the main axis spindle speed, in min1.
For example, when the spindle speed is 500min1 and the cutting length per minute is 120mm / min, what is the feed rate per revolution?
Answer: substitute n = 500 and I = 120 into the formula.
That is 0.24 mm / rev.
Rrε： Also recorded as re, corner radius of insert, unit: mm.
To understand the above formula, refer to the figure below.
Ra, Rz and Ry definitions
Ra: arithmetic mean deviation of contour, take the arithmetic mean of the absolute value of contour offset in degree L. Main evaluation parameters.
The average height between the peak and valley is R5 degrees, and the average height between the peak and valley is 5 degrees.
Generally, it is only used to represent relatively short and small surfaces.
Ry: the maximum height of the contour, taking the distance between the contour peak line and the contour bottom line in degree L.
It is basically not used alone. It can be regarded as a limit deviation value.
Arithmetic mean deviation Ra
Ra is calculated as follows:
When the roughness curve is represented by y = f (x), take the xaxis as the average line direction and the yaxis as the vertical magnification of the roughness curve.
When the magnification is within the range of the sampling reference length “ℓ”, it is represented by microns.
Ra can objectively reflect the geometric characteristics of the measured contour.
Ra value can be measured directly by electric profiler, but it is not intuitive.
Micro unevenness ten point height Rz
Rz is calculated as follows:
Rz can be obtained from the average distance between the average line and the five peaks (Yp) and the average value of each distance (Yv) between the average line and the five valleys (in microns).
Rz is used to evaluate the height parameters of surface roughness, which is intuitive and easy to measure on optical instruments, but it is limited to reflect the geometric characteristics of the measured contour.
Yp1, Yp2, YP3, yp4 and yp5 in the above figure are the distance from the average line to the highest five peaks within the sampling reference length “ℓ”.
Yv1, yv2, yv3, yv4 and yv5 are the distance from the average line to the lowest 5m valley within the sampling reference length “ℓ”.
Maximum height of contour Ry
Ry is calculated as follows:
Ry is derived from the distance (in microns) between the highest peak and the lowest valley within the sampling reference length (ℓ) to the mean line direction of the roughness curve.
Parameter Ry is easy to measure.
When the measured surface is very small and RZ is not suitable for evaluation, Ry can be used.
Root mean square RMS
The RMS is calculated as follows:
In the above formula:
L, the evaluation length
Z (x), as a function of contour height
The formula is approximately equivalent to:
RMS is the root mean square of the deviation of the contour length from the mean line and is recorded in the evaluation length.
Ra and RMS are both expressions of surface roughness, but their calculation methods are different.
Ra is calculated as the average peak and valley of the micro roughness of the surface.
RMS is calculated as the root mean square of the microscopic root mean square of the surface.
Each value is measured using the same surface peak and valley height measurements, but using different formulas.
Symbols and changes of Ra, Rz and Ry in JIS standard
Type  According to JIS B 06011994 standard  According to JIS B 06012001 standard 
Maximum height of the profiles  R_{y}  R_{z} 
Ten point height of irregularities  R_{z}  R_{zJIS} 
Arithmetic mean deviation of contour  R_{a}  R_{a} 
National definitions of surface accuracy and industrial standards (part)
China:
GB / T 3505 2000 surface roughness terms and parameters;
GB / T 10311995 surface roughness parameters and their values;
GB / T 1311993 mechanical drawing surface roughness symbols, codes and notes.
Japan:
JIS B 06012001, definition and name, jisb diagram. Surface roughness.
JIS B 06011982, definition and name, jisb diagram. Surface roughness, old version.
JIS B 00311982, definition and name, jisb diagram. Surface roughness, old version.
JIS B 00311994, definition and name, jisb diagram. Surface roughness, old version.
JIS B 06011994, definition and name, jisb diagram. Surface roughness, old version.
Britain:
BS EN ISO 4287:2000, definition of common parameters.
Germany:
Din 4768 (1990) standard for surface roughness in various fields (including metal castings).
Din 4771 (1977) measures the surface contour height P ₜ.
Din 4775 (1982) measures the surface roughness of the workpiece.
Din 4776 (1990) measuring surface roughness; Parameters R 1, R 4, RVK, MR1, MR2 are used to describe the material part in the roughness profile (profile bearing length ratio); Measurement conditions and evaluation procedures.
Din 4777 (1982) surface measurement; Contour filter of electric contact needle measuring instrument; Phase correction filter.
DIN ISO 1302 standard for surface roughness in various fields, including metal castings.
France:
NF e05015 (1984), geometrical product specifications (GPS) – surface texture: contour method – terms, definitions and surface texture parameters
NF e05016 (1978), geometric product specification (GPS) – surface texture indication in technical product documentation
NF e05017 (1972), surface condition of products and surface measurement method.
Europe:
EN 10049 2005, the European standard defines the measurement conditions of surface roughness parameters of metal flat products not coated (cold rolled and hot rolled pickled steel) and coated with metal coatings (e.g. zinc, aluminum, tin, chromium).
American national standard:
ASME B46. 12009, surface texture (surface roughness, waviness and position).
ASME B46. 11995, surface texture (surface roughness, waviness and position), old edition.
ASME B46. 11985, surface texture (surface roughness, waviness and position), old edition.
ANSI B4. 21978, surface texture. Surface roughness, undulation and undulation.
International standards:
ISO 13202002, the main standard, provides the definition of common parameters.
ISO 2517871:2012, geometrical specifications (GPS), surface texture
ISO 4681982, surface roughness – parameters, their values and general rules for specifying requirements
ISO 42871997, definitions of common parameters, such as those given by Rx.
ISO 4287/11984，
ISO 42881996, geometrical product specifications, contour method – rules and procedures for surface texture evaluation
ISO 42881985，
ISO 13201978，
ISO 120851996, contour method – pattern parameters.
Symbols and codes of surface roughness
Basic concepts
As shown in the figure below, the surface roughness value, cutoff value or reference length, processing method, grain direction, surface fluctuation, etc. are represented around the surface symbol.
a. Ra value
b. Processing mode
c. Critical value, evaluation length
C ´, reference length, evaluation length
d. Texture direction
f. Parameters other than Ra (e.g. parameters / cutoff level)
g. Surface fluctuation
Basic symbol style (JIS B 0610 and DIN ISO 1302, DIN 4768)
Materials to be removed during processing (JIS B 0610 and DIN ISO 1302, DIN 4768)
It is forbidden to remove materials during processing (JIS B 0610 and DIN ISO 1302, DIN 4768).
Preset the upper limit of RA (JIS B 0610 and DIN ISO 1302, DIN 4768)
Calibrate texture direction (JIS B 0610 and DIN ISO 1302, DIN 4768)
Preset the upper and lower limits of Ra (JIS B 0610 and DIN ISO 1302, DIN 4768)
Calibration processing method (JIS B 0610 and DIN ISO 1302, DIN 4768)
Comparison table of triangular symbols of surface roughness with Ra, Rz and Ry
Triangle symbol is a simple way to mark the accuracy grade of machined surface in machining design.
It should be noted that the finishing symbols (triangle ▽ and wave ~) are cancelled from the JIS standard revised in 1994.
Here is a brief introduction to the triangle symbol.
Ra unit µm  Ry unit µm  RzJIS unit µm  Triangle symbol 
0.0025 0.05 0.1 0.2  0.1 0.2 0.4 0.8  0.1 0.2 0.4 0.8  ∇∇∇∇ 
0.4 0.8 1.6  1.6 3.2 6.3  1.6 3.2 6.3  ∇∇∇ 
3.2 6.3  12.5 25  12.5 25  ∇∇ 
12.5 25  50 100  50 100  ∇ 
Comparison table of surface roughness
Rz (µm)  VDI3400  Ra (µm)  RMS (µinch)  Class ISO 1302 
0.08  –  0.0125  0.5  
0.16  –  0.025  1  
0.32  –  0.05  2  
0.64  0  0.10  4.1  N3 
0.70  1  0.11  4.5  
0.76  2  0.12  4.9  
0.90  3  0.14  5.7  
1.02  4  0.15  6.6  
1.15  5  0.17  7.4  
1.28  6  0.20  8.2  N4 
1.41  7  0.23  9.0  
1.60  8  0.25  10.2  
1.79  9  0.28  11.5  
2.05  10  0.32  13.1  
2.24  11  0.35  14.3  
2.56  12  0.40  16.4  N5 
2.88  13  0.45  18.4  
3.20  14  0.50  20.5  
3.58  15  0.56  22.9  
4.03  16  0.63  25.8  
4.48  17  0.70  28.7  
5.12  18  0.80  32.8  
5.76  19  0.90  36.9  N6 
6.40  20  1.00  41.0  
7.17  21  1.12  45.8  
8.06  22  1.26  51.6  
8.96  23  1.40  57.3  
10.24  24  1.60  65.5  
11.52  25  1.80  73.7  N7 
12.80  26  2.00  81.9  
14.08  27  2.20  90.1  
16.00  28  2.50  102.4  
17.92  29  2.80  114.6  
20.48  30  3.20  131.1  N8 
22.40  31  3.50  143.4  
25.60  32  4.00  163.8  
–  33  4.50  –  
32.00  34  5.00  204.8  
–  35  5.60  –  
40.32  36  6.30  258.0  N9 
–  37  7.00  –  
51.20  38  8.00  327.7  
–  39  9.00  –  
64.00  40  10.00  409.6  
–  41  11.20  –  
–  42  12.60  –  N10 
–  43  14.00  –  
–  44  16.00  –  
–  45  18.00  – 
*VDI：Verein Deutscher Ingenieure
*RMS：Root mean square
Comparison table of processing methods and processing accuracy
Symbol
 ○ Default machining (standard)
 ● Precision
 ◇ Rough machining
 ◈ Medium
 ◆ Fine
Ra arithmetic mean 
0.025 
0.05 
0.1 
0.2 
0.4 
0.8 
1.6 
3.2 
6.3 
12.5 
25 
50 
100 

Ry maximum peak 
0.1 
0.2 
0.4 
0.8 
1.6 
3.2 
6.3 
3.2 
12.5 
25 
100 
200 
400 

Evaluation length mm 
0.25 
0.8 
2.5 
8 
25 

Triangle indication 
∇∇∇∇ 
∇∇∇ 
∇∇ 
∇ 
– 

Processing technology

Forging 







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Casting 







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Die casting 







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Cold rolling 


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Drawing 





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Extruding 





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Tumbling 

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Sandblasting 







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Rolling 



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Face cutter grinding 





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Planing 







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Carving Slotting 







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Cutter grinding 





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Precision boring 



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Filing 





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Round grinding 


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Boring 





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Drilling 







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Reaming 




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Broach grinding 




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Shaving 





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Grinding 


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Hone finishing 


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Super finishing 
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Buffing 

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Paper finishing 


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Lapping 
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Liquid honing 


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Burnishing 



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Surface rolling 



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Electric discharge carving 





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Wire cut electric spark 






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Chemical polishing 




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Electrolytic abrasion 
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