## D roughness parameters

The range of parameters calculated from a trace may be represented by the equation:

parameter = TnN

where:

■ 'T' represents the scale of the parameter. If the trace is unfil-tered, the designation 'P' is used. After filtering, the parameters calculated are given the designation 'R' for roughness or 'W' for waviness. If parameters relate to an area, the designation 'S' is used.

■ 'n' represents the parameter suffix which denotes the type calculated, e.g. average is 'a', RMS is 'q', Skew is 'sk', etc.

■ 'N' refers to which of the five SLs the parameter relates to, e.g. the RMS value of the third sample is Rq3.

Over the years, hundreds of roughness parameters have been suggested. This has prompted Whitehouse (1982) to describe the situation as a 'parameter rash'! The standard ISO 4287:1997 defines 13 parameters which are shown in the table in Figure 6.7. These parameters are the most commonly used ones and the ones accepted by the international community as being the most relevant. They are divided into classes of heights, height distribution, spacing and angle (or hybrid). It should be noted that there are other parameters, based on shapes of peaks and valleys, which are more relevant to specific industries like the automotive (ISO 13565-2:1996 and ISO 12085:1996).

### 6.3.1.1 2D amplitude parameters

The table in Figure 6.8 gives the definitions of the ISO 4287:1997 height parameters. The centre line average (Ra) is the most common. It is defined in ISO 4287:2000 as the 'arithmetic mean deviation of the assessed profile'. Over an EL, there will normally be five Ra values, Ral to Ra5. The root mean square (RMS) parameter (Rq) is another average parameter. It is defined in ISO 4287:1997 as the 'root mean square deviation of the assessed profile'. There will normally be five Rq values: Rql to Rq5. The Rq parameter is statistically significant because it is the standard deviation of the profile about the mean line.

 PARAMETER CLASS PARAMETERS IN ISO 4287 Heights Ra, Rq, Rv, Rp, Rt, Rz, Rc Height Distribution Rsk, Rku, Rmr, Rmr(c) Spacing Rsm Hybrid RAq

Figure 6.7 The 2D roughness parameters given in ISO 4287:2000

Figure 6.7 The 2D roughness parameters given in ISO 4287:2000

With respect to parameters which measure extremes rather than averages, the Rt parameter is the value of the vertical distance from the highest peak to lowest valley within the EL (see Figures 6.8 and 6.9). It is defined in ISO 4287:1997 as the 'total height of profile'. There will be only one Rt value and this is THE extreme parameter. It is highly susceptible to any disturbances. The maximum peak to valley height within each SL is Rz (see Figures 6.8 and 6.9). It is defined in ISO 4287:1997 as the'maximum height of the profile'. There are normally five Rz values, Rzl to Rz5, or Rzi. With reference to the fine-turned profile of Figure 6.6, the Rzi values are shown as Ryi, a former designation.

Material above and below the mean line can be represented by peak and by valley parameters (see Figures 6.8 and 6.9). The peak parameter (Rp) is the vertical distance from the highest peak to the

 PROFI LE HEIGHT PARAMETERS Parameter Description Ra Centre Line Average Ra-ISW^lHdx Rq RMS Average Rt EL peak to valley height Peak to valley height within the EL Rz SL peak to valley height Peak to valley height within a SL hp Peak height Highest peak to mean line height Rv Valley depth Lowest valley to mean line depth

Figure 6.8 The 2D height parameters given in ISO 4287:2000

Figure 6.8 The 2D height parameters given in ISO 4287:2000 SL1 I SL2 SL3 SL4 SL5

Figure 6.9 A schematic profile and the parameters Rt, Rz, Rv, Rp

### SL1 I SL2 SL3 SL4 SL5

Figure 6.9 A schematic profile and the parameters Rt, Rz, Rv, Rp mean line within a SL. It is defined in ISO 4287:1997 as the 'maximum profile peak height'. The valley parameter, Rv, is the maximum vertical distance between the deepest valley and the mean line in a SL. It is defined in ISO 4287:1997 as the 'maximum profile valley depth'.

### 6.3.1.2 2D amplitude distribution parameters

With respect to a profile, the sum of the section profile lengths at a depth 'c' measured from the highest peak is the material length (Ml(c)). In ISO 4287:1997 the parameter Ml(c) is defined as the 'sum of the section lengths obtained by a line parallel to the axis at a given level, "c"'. This is the summation of 'Li' in Figure 6.5. If this length is expressed as a percentage or fraction of the profile, it is called the 'material ratio' (Rmr(c)) (see Figure 6.10). It is defined in ISO 4287:1997 as the 'ratio of the material length of the profile elements Ml(c) at the given level "c" to the evaluation length'. In a previous standard, this Rmr(c) parameter is designated 'tp' and can be seen as TP 10 to TP90 in the fine-turned BAC of Figure 6.6.

The shape and form of the ADF can be represented by the function moments (m ):

where N is the moment number, y. is the ordinate height and 'n' is the number of ordinates. The first moment (mt) is zero by definition. The second moment (m2) is the variance or the square of the

 PROFILE HEK Parameter 3HT DISTRIBUTION PARAMETERS Description Rmr(c) Material ratio at depth 'c' Rmr(c) = ^ 2 Li = ¿n> Rsk Skew Rsk = — Rq3 1 " L 0 Rku Kurtosis Rku = ——-r Rq4 ." 1=1 L 0

Figure 6.10 The 2D height distribution parameters given in ISO 4287:2000

Figure 6.10 The 2D height distribution parameters given in ISO 4287:2000

standard deviation, i.e. Rq. The third moment (m3) is the skew of the ADF. It is usually normalised by the standard deviation and, when related to the SL, is termed Rsk. It is defined in ISO 4287:1997 as the 'skewness of the assessed profile'. For a random surface profile, the skew will be zero because the heights are symmetrically distributed about the mean line. The skew of the ADF discriminates between different manufacturing processes. Processes such as grinding, honing and milling produce negatively skewed surfaces because of the shape of the unit event/s. Processes like sandblasting, EDM and turning produce positive skewed surfaces. This is seen in the fine-turned profile in Figure 6.6 where the Rsk value is +0.51. Processes like plateau honing and gun-drilling produce surfaces that have good bearing properties, thus, it is of no surprise that they have negative skew values. Positive skew is an indication of a good gripping or locking surface.

The fourth moment (m4) of the ADF is kurtosis. Like the skew parameter, kurtosis is normalised. It is defined in ISO 4287:1997 as the 'kurtosis of the assessed profile'. In this normalised form, the kurtosis of a Gaussian profile is 3. If the profile is congregated near the mean with the occasional high peak or deep valley it has a kurtosis greater than 3. If the profile is congregated at the extremes it is less than 3. A theoretical square wave has a kurtosis of unity.

### 6.3.1.3 2D spacing parameters

Figure 6.11 shows a schematic profile of part of a surface that has been turned at a feed of 0,1 mm/rev. The cusp profile is modified by small grooves caused by wear on the tool. The problem with this profile is that there are 'macro' and 'micro' peaks, the former being at 0,1mm spacing and the latter at 0,011mm spacing. Either could be important in a functional performance situation. This begs the question, 'when is peak a peak a peak?' To cope with the variety of possible situations, many spacing parameters have been suggested over the years. However, it is unfortunate that in the ISO standard only one parameter is given. This is the average peak spacing parameter RSm that is the spacing between peaks over the SL at the mean line. It is defined in ISO 4287:1997 as the 'mean value of the profile element widths within a sampling length'. With respect to Figure 6.11, if the 0,2mm were the SL, there are 10 peaks shown and hence RSm = 0,02mm.

### 6.3.1.4 2D slope parameters

The RMS average parameter (RAq) is the only slope parameter included in the ISO 4287:1997 standard. It is defined as the 'root mean square of the ordinate slopes dz/dx within the sampling length'. There will normally be five RAq values for each of the SL values: RAql to RAq5. The RAq value is statistically significant because it is the standard deviation of the slope profile about the mean line. Furthermore, the slope variance is the second moment of the slope distribution function. In theory, there can be as many slope parameters as there are height parameters because parameters can be just as easily be calculated from the differentiated profile as from the original profile.

Figure 6.11 The 2D spacing parameter given in ISO 4287:2000

Figure 6.11 The 2D spacing parameter given in ISO 4287:2000

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