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Surface Roughness  Surface Roughness is a component of Surface Texture. It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form. If these deviations are large, the surface is rough; if they are small, the surface is smooth.

Surface texture is the appearance of the surface which may comprise of error of Form, Waviness, and Roughness.

Roughness has very high frequency irregularity and can be caused by tool marks, feed marks or abrasions depending on the metal process used.

Surface roughness of a machining part has been used to define the product as “smooth” or “rough”. In the production area where a part is machined by using a lathe, milling or grinding machine to inspect of each surface roughness, the operator will use his/her finger to “feel” it as compared with the roughness plate scale value. The engineer will have difficulty in deciding the value.

Now with the help of computers, many engineering problems can be solved. We can easily get the value of surface roughness which refers to international standards such as JIS. Many parameters of roughness can be used to define the value, such as using Ra or Rz.

Below, we will illustrate how to calculate Ra and Rz according to the graphic curve of roughness measurement which has been done by using Surfcom Nex 001.

Measurement Result We measure a Roughness Specimen to get the roughness graph and result of Ra.

Definition of Ra is the average deviation deviding the area of the part to be surrounded by the sampling curve and the average line by the sampling length (JISB0601:2001).

The formula is given below:
l
Ra  = 1/n ? [Z(x)] dx
0
where
Z(x): The absolute average in the part having taken out only sampling length
X: The Mean line direction
? (n): The range of sampled reference length
RP: Levels of average roughness peak
RV: Levels of average roughness valley

According to formula of Ra and roughness graph above, here is the way to calculate the result:

Ra  = (RP1+RP2+ ...+RPn)+(RV1+RV2+ ... +RVn)
n
Ra = (3.5 + 4 + 3 + 3.5 + 3 + 4 + 3 + 3.5 + 3 + 4 + 3 + 3.5 + 2.5 + 4 + 3 + 4 + 3 + 4 + 2.5 + 3.5 + 3 + 3.5 + 3 + 3.5 + 3 + 3.5 + 2.5 + 3.5 + 2) + (2 + 3.5 + 2.5 + 3.5 + 2.5 + 3.5 + 2.5 + 4 + 3.5 + 3.5 + 2.5 + 3.5 + 2.5 + 3.5 + 2.5 + 4 + 3 + 3.5 + 2 + 3.5 + 2 + 3.5 + 3 + 3.5 + 3 + 3.5 + 3 + 3.5 + 2.5 + 4) / 61

Ra = (101.5) + (93)/61

Ra = 194.5/61

Ra = 3,188µm

* Conclusion: the result value of Ra from Surfcom Nex 001 with calculation data of graphic curve is similar. The same result of Roughness Specimen measurement is Rz.

Definition of Rz is the sum of the maximum value (RP) of the peak height (ZP) and the maximum value (Rv) of the valley depth (ZV) of the profile in the sampling length (JISB0601:2001).

The formula is given below:

Rz = RP + RV = max[Zpi] + max[Zvi] = max[Z(x)] + min[Z(x)]

where
RP: The maximum value of the peak height
RV: The maximum value of the valley depth

According to formula of Rz and roughness graph above, here is the way to calculate the result:

RZ = (RP1+RP2+...+RP5)+(RV1+RV2+...+RV5)
5
Rz = (5+5+5.1+5+5) + (5+5+5.1+5.1+5.1)
5
Rz = (25.1)+(25.3)
5
Rz = 50.4/5
Rz = 10.08µm.

* Conclusion: the result value of Rz from Surfcom Nex 001 with calculation data of graphic curve is similar.

Notes
• Calculations using JIS 2001 based on customer requests to know how roughness results in roughness equipment compares with roughness graphic curve calculations. Example measurement of roughness specimen (Ra and Rz) using Surfcom Nex 001.
• Difference of Ra and Rz calculations from Surfcom Nex 001 from calculations of graphic curve is due to reading values of Rp and Rv graphic curve not close to actual result.
• For Ra definition, please refer to Application Guide Manual for Surfcom Series, code: DT0300-R001-E13, page 5-1 by Accretech (Tokyo Seimitsu Kikai).
• For Rz definition, please refer to Application Guide Manual for Surfcom Series, code: DT0300-R001-E13, page 5-6 by Accretech (Tokyo Seimitsu Kikai).

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