While Measuring Roughness: Ra

6 Practical Tips for Laboratory & Workshop

A perfect surface is a mathematical abstraction, as any actual surface, perfect enough, present irregularities arising during the manufacturing process.

Major irregularities (macrogeometrics) form errors are associated with variation in size of a piece, flatness and parallelism between surfaces of a surface or taper, roundness and cylindricity, and that can be measured with conventional instruments. Minor irregularities (microgeometrics) are waviness and roughness. The first bending can be caused in workpiece during machining, material hardness or inhomogeneities, residual stress, deformation by thermal treatment, vibrations… while waviness and roughness can be product of the element used for machining: cutting tool or the grinding stone.

 

Surface mentioned errors occur simultaneously on a surface, which hinders the individual measurement of each.

Roughness (which is the fingerprint of a piece) are irregularities caused by the cutting tool or element used in the production process, cut, starting and surface fatigue.

 • 1.- Profiles and filters (EN ISO 4287 & EN ISO 166210)

The measured actual surface profile results from the intersection of the actual part surface with a plane perpendicular to this surface. The plane should roughly be vertical to the machining grooves.

IMG_20160120_230153.jpg
PhotoCredits: Mitutoyo Leaflet & Flyer

Measured surface profile is the profile after tracing the actual surface profile using a probe. In doing so, the measured values are filtered through the effect of the stylus tip radius rtip and – where applicable – through the sliding skid of the probe system. Imperfections of the surface, like cracks, scratches and dents do not count as roughness and should not be measured. If necessary, tolerances must be determined for this according to EN ISO 8785.

 

Herstellverfahren und Rauheit von Oberflächen. Rightlinien für Konstruktion und Fertigung
Herstellverfahren und Rauheit von Oberflächen. Rightlinien für Konstruktion und Fertigung

Primary profile is the profile after low-pass filtering the measuring values using the cutoff wavelength λs. In doing so, the short-wave profile parts are cutoff. The parameters are identified by P and evaluated within the sampling length (cut-off). This equals the measured length or the length of the measured surface profile.

 

 

 

 

 

 

Fig. 1: Primary profile after λS low-pass filtering

Roughness profile results from high-pass filtering the primary profile with the cutoff wavelength λc. In doing so, the long-wave profile parts are cut-off. The parameters are identified by R and evaluated over the measured length ln which is usually composed of five single measured lengths lr. The single measured length corresponds to the cutoff wavelength λc of the profile filter.

Fig. 2: Roughness profile after λC high-pass filtering with center line representation according to EN ISO 4287

The waviness profile results from low-pass filtering the primary profile with the cutoff wavelength λc and high-pass filtering with the cutoff wavelength λf. The parameters are identified by W and evaluated over the measured length In which is composed of several sampling lengths lw.The single measured length Iwcorresponds to the cutoff wavelength λf of the high-pass filter.

However, their number is not standardized and must therefore always be indicated on the drawing. It should range between five and ten. Profile filters λc (Fig. 3) and λf are applied successively. The waviness profile always results from application of both filters (Fig. 4).

The roughness profile results from high-pass filtering the primary profile with the cutoff wavelength λc. In doing so, the long-wave profile parts are cut-off. The parameters are identified by R and evaluated over the measured length ln which is usually composed of five single measured lengths lr. The single measured length corresponds to the cutoff wavelength λc of the profile filter.

Fig. 3: Representation after λc low-pass filtering

Fig. 4: Waviness profile after λc low-pass filtering and λf high-pass filtering with center line representation according to EN ISO 4287

Fig. 5: Transmission characteristics of the filters for the different profiles, Gaussian filter according to EN ISO 11562

• 2.- Roughness Parameters (EN ISO 4287 & EN ISO 16610)

Ra – Arithmetic mean surface roughness: Arithmetical mean of the sums of all profile values

Rmr(c) – Material proportion of the profile: Quotient from the sum of all material lengths of the profile elements at the specified section height c (in μm) and the measured length ln (specified in per cent)

RSm – Average groove width: Mean value of the width of the profile elements Xsi (formerly Sm); for the evaluation, horizontal and vertical counting thresholds are determined.

Rt – Total height of the roughness profile: Sum from the height Zp of the highest profile peak and the depth Zv of the lowest profile valley within the measured length ln

Rzi – Maximum height of the roughness profile: Sum from the height of the highest profile peak and the depth of the lowest profile valley within a sampling length lri

Rz1max – Maximum surface roughness: Largest of the five Rzi-values from the five sampling lengths lri over the total measured length ln

Rz – Surface roughness depth: Mean value of the five Rzi-values from the five sampling lengths lri over the total measured length ln

Fig. 6: Arithmetic average roughness value Ra

Fig. 7: Total height of the roughness profile Rt, surface roughness depth Rz and maximum surface roughness Rz1max

Fig 8: The average groove width RSm is the mean value of the width Xsi of the profile elements

Fig. 9: The material ratio curve of the profile plots the material portion Rmr(c) of the profile as a function of the section height c (Abbott-Firestone curve)

• 3.- Preferred Parameters In Surface Roughness Measurements

Maximum surface roughness Rz1max for surfaces where individual deviations heavily affect the function of the surface, e.g. sealing surfaces

Material portion of the profile Rmr(c) for guide surfaces and sealing surfaces moving against each other

Surface roughness depth Rz, as a rule, is used for all other surfaces

The arithmetic average roughness value Ra hardly reacts to peaks or valleys due to the mean value formation from all profile values so that its significance is rather low. Note also the unit conversion ratio:  1 µInch  ­­= 25,40001 µm unless in UK where becomes 25.39978 µm as shown below:

Where AA : Arithmeric Average
CLA : Center Line Average
Rq : Geometric average roughness
RMS : Root-Mean-Square

• 4.- Fits & Conditions 4 Surface Roughness Measurements (EN ISO 4288)

• 5.- Evaluation of Roughness Measurements (EN ISO 4288)

Roughness measuring values – especially the vertical parameters (amplitude parameters) Rt, Rz, Rz1max and Ra – have a spread between -20 % and +30 %. A single measuring value can therefore not provide a complete statement concerning the observance of the permissible parameter tolerances. EN ISO 4288 Appendix A specifies the following procedure:

Max-rule: All roughness parameters with the addition “max“ as maximum value of the average value from the five single measured lengths: Measurement at least three points on the surface where the highest values are to be expected; the limit value must not be exceeded at any point.

16 %-rule: All roughness parameters without the addition “max“ as mean value from the five single measured lengths: 16 % of the measuring values may exceed the limit value; step-by-step procedure:

  1. If the first measuring value is smaller than 70% of the limit value, is considered to be OK.
  2. Otherwise two further measurements at other points on the surface; if all three measuring values are smaller than the limit value, is considered to be OK.
  3. Otherwise nine further measurements at other points on the surface; if no more than two measuring values exceed the limit value, is considered to be OK.

    • 6.– Drawing symbols (EN ISO 1302)

EGA is registered 14.302 Engineer C.O.I.T.I.M

 

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