Calibration of Roughness Parameters

Profile method

Theoretical bases

In roughness metrology, the surface is scanned with a stylus instrument in accordance with ISO 3274 profile method). A stylus instrument is a measuring instrument which scans surfaces with a stylus tip, determines deviations in the form of a surface profile and calculates parameters. In addition it is in a position to record profiles. The block diagram (Figure 1) below only shows the components required for a theoretically exact measuring system.

Figure 1. Schematic view of a stylus instrument
1 -surface, 2 -stylus tip , 3 -traced profile, 4 -mechanical-electrical transducer, 5 -measurement loop,
6 -guide, 7 -reference profile, 8 -external disturbances, 9 -traverse, 10 -amplifier, 11 -ADC,
12 -total profile, 13 -elimination of the nominal form, 14 -profile filter λs, 15 -primary profile, 16 -evaluation device, 17 -input/output, 18 -input/output, 19 -pick-up, 20 -vertical profile transmission,
21 -drive unit

The traced profile is the locus of the centre of a stylus tip as it traverses the surface within the intersection plane. This stylus tip has a geometrically ideal form with nominal sizes and nominal measuring force (see Figure 2).

Figure 2. Stylus tip recorded with a scanning electron microscope

From this profile, all other profiles defined in the standards have been derived. A trace on which the probe is moved within the intersection plane along the guide is defined as the reference profile. The total profile is a digital form of the traced profile relative to the reference profile, with the vertical and horizontal coordinates assigned to each other. To be able to obtain a primary profile, a filter for short wavelengths(λs) must be applied to the total profile. The primary profile represents the basis for digital profile processing by means of a profile filter according to ISO 11562 and calculation of surface parameters. It is characterized by the vertical and horizontal digital steps which may deviate from those of the total profile. Application of the least squares method to the line of the specified nominal form (best fit least squares form) is not part of the determination of the primary profile and is performed before filtering. The primary profile does not contain any nominal form.
A measurement loop is a closed chain which contains all mechanical components connected with the specimen and the stylus tip (positioning devices, specimen holder, feed device, pick-up, etc.). A pick-up is a sub-assembly which contains the tracing element with the stylus tip and the mechanical-electrical transducer. The sub-assembly which moves the probe along the reference guide and transmits the horizontal position of the stylus tip in the form of a horizontal profile coordinate, is the drive unit.

Profile filtering and evaluation

Profile filtering and evaluation refer to calculations performed with the aid of parameters and characteristic functions in accordance with ISO 4287,
ISO 11562, ISO 12085, ISO 13565-1,2,3 on the primary, roughness and waviness profile.
The evaluation principle in roughness measurement is explained by an example.

The traced profile

The aligned profile filtered with λs (P-profil)

The waviness profile (W-profil)

The roughness profile (R-profil)

Figure 3. Example of the evaluations in roughness measurement, which P-profil = R-profil + W-profil 

Surface parameters

Surface parameters can be subdivided into five groups:

Vertical parameters (amplitude parameters) in accordance with ISO 4287 (peak heights and valley depths)

• Largest profile peak height within a sampling length Pp, Rp, Wp
• Largest profile valley depth within a sampling length Pv, Rv, Wv
• Größte Höhe des Profils innerhalb der Einzelmessstrecke Pz, Rz, Wz
• Mean height of the profile elements within a sampling length Pc, Rc, Wc
• Total height of profile within the evaluation length Pt, Rt, Wt

Vertical parameters (amplitude parameters) in accordance with ISO 4287 (average of ordinates)

• Arithmetic mean of the absolute ordinate values within a sampling length Pa, Ra, Wa
• Root mean square value of the ordinate values within a sampling length Pq, Rq, Wq
• Skewness of the profile within a sampling length Psk, Rsk, Wsk
• Kurtosis of the profile within a sampling length Pku, Rku, Wku

Horizontal parameters (spacing parameters) in accordance with ISO 4287

• Mean width of the profile elements within a sampling length PSm, RSm, WSm

Hybrid parameters

• Root mean square slope of the profile within a sampling length P∆q, R∆q, W∆q

Characteristic curves and related parameters according to ISO 4287 and ISO 13565-1,2

All curves and related parameters are defined over evaluation length.

• Material ratio of the profile Pmr(c), Rmr(c), Wmr(c)
• Material ratio curve of the profile (Abbott Firestone curve)
• Height difference between two profile section levels Pδc, Rδc, Wδc
• Relative material ratio Pmr, Rmr, Wmr
• Amplitude density curve
  
• Core roughness depth Rk
  
• Material portion Mr1, Mr2
• Reduced peak height Rpk
• Reduced valley depths Rvk