Interpretation of “Rz = 4×Ra” and other roughness parameters in the evaluation of machined surfaces

Béla Palásti-Kovács1, Sándor Sipos1, Árpád Czifra1

Abstract

The above mentioned roughness calculation formula is considered as a starting point in the nowadays industrial practice and in certain parts of the current curriculum, used in the training of the technician experts of secondary and higher education. Our present work examines some areas in connection with this formula. It introduces that the different machining operations result in different surface microgeometries and in different Rz/Ra-ratios. It points out that the wear development and any change in the edge condition cause significant differences in the arithmetical, average values and in the form of the surface microgeometry. With the help of examples it demonstrates the uncertainties of the surface roughness measurement technology during the evaluation of the real and filtered surface profiles.

In the design process of machines we can meet calculating methodes, developed several decades ago. The revision of the connection between tolerance and surface roughness has not taken place parallel with the essential development of surface microgeometry characterization. The long-standing Ra-Rz recalculations are generally used in this case as well, although the determination of the surface roughness is one of those tasks, causing an immediate improvement in the working efficiency of improvement in the working efficiency of machines. Possessing the new knowledge it requires a careful consideration to apply the surface roughness parameters their numerical values in an appropriate way.

This article was firstly published at the 13th International Conference on Tools (ICT-2012), held in Miskolc (Hungary), on 27-28 March 2012, printed in the official issue of the Proceedings, p. 237-244. (ISBN 978 - 963 - 9988 - 35 - 4)

Introduction

Nowadays, the role of surface quality has become extremely important in design of machines and production of components. The microgeometry (roughness, waviness), i.e. the better measurable and better manageable side of surface quality, shows up widely in researches, carried out in order to get to know the tribological behaviour and the operation of machine parts, connecting with each other. They will be considered during the measuring processes, in specifications, concerning engineering drawings and in case of creating models as well. The available roughness standards (ISO 4287:1997) mean a wide range of parameters, to be followed by the engineers when creating engineering drawings. Some comprehensive articles [1, 2], prepared in Hungary, have shown that almost Ra and Rz parameters are exclusively used in the industrial practice in Hungary and abroad as well in order to qualify working surfaces.

The so-called amplitude parameters (Ra, Rz) have been a well-known factors for designing and producing engineers for decades, they serve as a basis of the measuring model, they reflect a known and well-proven experience in machining, so their application seems to be a reliable solution. Parallel with the dynamic development of manufacturing technology and surface finishing processes, the machines of present times can be characterised by such new technical surfaces, being different in their character and quality, and having been consciously planned and produced, when the principles, having been well-proven earlier, are losing in their importance or they require a careful consideration. In our present work we are going to show some examples in order to think over these reflections.

What is shown in the industrial practice?

The increased quality requirements, concerning of the 21st century, expect from the technical experts to identify the surface roughness not only with Ra or Rz roughness parameters, but with „deeper“ quality requirements of the connecting surfaces as well in order to improve the product further. Something else is shown in the industrial practice (Fig. 1.) [3].

Roughness parameters, measured in the industrial practice

We can observe in the manufacturing technology of world that the arithmetical parameters (Ra, Rz, Rt and Rp) are dominant and other attributes, describing the working behaviour in a better way, are still pushed into the background. The drawings, prepared on the components, contain mainly only one parameter, therefore the following question can arise: Can we reconvert one parameter into the other one for sure? Is there a correlation, for example, between Ra and Rz, to be used in case of machining and describable by a certain formula?

The formulas „Rz=4×Ra“, or „Rz=4.5×Ra“, given in the title of our present article, have been determining the professional training and the practical lessons of manufacturing technology at least for six-seven decades. Occasionally there are publications, revising and trying to modify this way of thinking [4, 5, 6], but till now they could not have achieved a real breakthrough in this question. If we analyse the roughness of surfaces, machined with different methods, we get the values, given in Table 1.. As it can be seen well, there is a significant difference in the ratio of Rz/Ra as the measured values scatter in a range of 4.91 and 9.2 .

Table 1. Roughness of surfaces, machined with different methods

Surface, machined by slot milling

Surface, machined by water jet cutting

Shaft of milling cutter, machined by grinding

Axle, machined by

super finishing

Ra

Rz

Rz/Ra

Ra

Rz

Rz/Ra

Ra

Rz

Rz/Ra

Ra

Rz

Rz/Ra

0.39

2.09

5.36

2.36

11.58

4.91

0.15

1.3

8.67

0.05

0.46

9.2

0.31

1.72

5.55

3.86

20.45

5.3

0.15

1.29

8.6

0.07

0.53

7.57

0.29

1.69

5.83

4.08

28.52

6.99

0.15

1.25

8.33

0.07

0.53

7.57

The values, given in the table, refer to the fact that the tool edges, the technical data of cutting operation, furthermore, the machining system and its surroundings 'produce' surfaces, having extremely different microgeometrical characteristics. The microgeometrical profile of surfaces, machined by turning, EDM, grinding and superfinishing operation, is shown in Figure 2. The differences can be seen well in every case and it means that we can talk about surfaces, having extremely different shape characteristics and ratio of Rz/Ra.

Milled surface, ra=0.36 μm, rz=2.11 μm

Milled surface, Ra=0.36 μm, Rz=2.11 μm

EDM surface, ra=0.43 μm, rz=2.95 μm

EDM surface, Ra=0.43 μm, Rz=2.95 μm

Grinding surface, ra=0.39 μm, rz=3.00 μm

Grinding surface, Ra=0.39 μm, Rz=3.00 μm

Superfinishing surface, ra=0.38 μm, rz=3.16 μm

Superfinishing surface, Ra=0.38 μm, Rz=3.16 μm

Figure 2. Various machined surface roughness profiles, Ra=0.36 … 0.43 μm, Rz/Ra=5.8 … 9.5

Our experiences in machining operation

In the past years we have carried out lot of tests on work pieces, having different degree of machinability, with tools of up-to-date construction and material.

Turning operation of modern engineering plastics

During finish-turning operation, the material and the rheological features of plastics can decisively affect the roughness of the surface, machined with turning operation. In case of low depth of cut values (a=0.5 mm) and with increase of the feed rate there is almost no change in the ratio of Rz/Ra in case of some materials (PET, POMC), while in case of other material types ((PA6, PEEK) an obvious decrease can be noticed. This ratio varies between 3.4-7.5, depending on the type of machined material and applied cutting conditions. Some of the examples, chosen by us from our tests, carried out by us systematically, can be seen in Fig. 3..

Surface roughness parameter ratios in case of turning operation of advanced plastics [7] Surface roughness parameter ratios in case of turning operation of advanced plastics [7]

Figure 3. Surface roughness parameter ratios in case of turning operation of advanced plastics [7]

Results, measured in case of environmental-friendly turning operation

The different types of green machining cause almost no or just a minimal pollution. During our turning tests we have applied five different types from air cooling methods (dry machining, cooling with compressed air, feeding N2-gas with a pressure of 6 bar, blowing compressed cold air with CAG-device). On the inserts, having K20 material and made by TaeguTec (South Korea), have been deposited by Platit AG (Switzerland) with modern (μAlTiN) PVD-coating. Figure 4. shows that although every cooling method has produced surfaces, having similar characteristic signs, the ratio of Rz/Ra varies in a range of 6.5 … 3.9. The character of change is clear: it can be modelled by power function regression with a great security assurance and in a reproducable way.

Rz/Ra ratio during environmental-friendly turning operation

Figure 4. Rz/Ra ratio during environmental-friendly turning operation

Effects of tool wear on the machined surfaces in case of hard part turning operation

The deterioration process of ceramic and CBN-inserts, used to the longitudinal turning operation of hardened steels, results in the change of the surface microgeometry. Analysing the diagrams (Figure 5.), the following facts can be noticed: the ceramic insert with wiper edge form has produced surfaces, having a ratio of Rz/Ra around 4.3 in the very first minutes of the deterioration process, while at the strongly-marked flank wear development this ratio has varied in a range of 6 ... 7.5. During the further wear process of tool edge the development of an 'ironing edge section' can be noticed and it results in the decrease of this ratio (Figure 5/a).

Hard part turning with ceramics

5/a. Hard part turning with ceramics

Hard part turning with boron nitride

5/b. Hard part turning with boron nitride

Figure 5. Rz/Ra surface roughness parameters versus the tool degradation process

The very first minutes (the so-called break-in period) of deterioration process of the ISO-shaped CBN-insert can be characterised by the decrease of Rz/Ra-ratio, after that an increase can be noticed in the ratio of Rz/Ra (from 4.5 up to 6.2) due to the 'chipping' of the edge. The edge condition is reflected by the size and character of the flank wear, and it is in a close connection with the ratio of the amplitude parameters. After the occurrence (tc=8 min) of phenomenon of layer changing [8] a continuous change can be noticed in the character of the machined surface as an 'ironing edge section' has started to develop, after that another changing the edge causes the oscillation of Rz/Ra-ration in the range of 5 ... 6 (Figure 5/b).

The surface roughness profile pictures, made during our earlier examinations, expressively show significant changes, developing during the machining time and caused by the continuous (not controllable) change in the tool edge and flank wear process (Figure 6.).

Changes of turned surface profile during the tool life [1]

Figure 6. Changes of turned surface profile during the tool life [1]

Table 2. The change of Ra, Rz and Rz/Ra, in function of machining time[1]

vc=250 m/min

rε=0.8

a=0.4

f=0.1 mm

vc=250 m/min

rε=0.8

a=0.4

f=0.15 mm

tc - machining time

Ra

Rz

Ratio of Rz/Ra

tc - machining time

Ra

Rz

Ratio of Rz/Ra

Theoretical value

0.4

1.56

3.9

Theoretical

value

0.88

3.66

4.2

0 min

0.65

3.63

5.6

0 min

1.3

6.04

4.6

1 min

0.74

3.7

5.0

1 min

1.34

5.83

4.4

2.5 min

0.69

4.33

6.3

2.5 min

0.95

5.71

6.0

5 min

0.86

4.7

5.5

5 min

0.82

5.83

7.1

10 min

1.18

6.31

5.3

10 min

0.71

4.26

6.0

15 min

1.59

9.75

6.1

15 min

1.2

8.01

6.7

20 min

1.91

9.06

4.7

20 min

1.5

8.34

5.6

Max.measured

1.91

9.75

6.3

Max.measured

1.5

8.34

7.1

Min. measured

0.65

3.63

4.7

Min.measured

0.71

4.26

4.4

Ratio of max.-min.

2.9

2.7

1.3

Ratio of max.-min.

2.1

2.0

1.6

Some characteristical changes in Ra, Rz and Rz/Ra values are summarised in Table 2.. The nose radius section, determining the surface roughness, has become nearly straight (in the period of 2.5-10 min), after that as a result of the edge wear, the roughness peaks have started to increase again. This phenomenon cannot be made universal, but can be made probable. From the tests it has become clear that depending on the conditions of wear development, the ratio Rz/Ra varies between 4.4 … 7.1, i.e. a change of 30-60% can be observed in the ratio during the deterioration process. A change of 200-270% can be calculated between the minimal and maximal value of Rz, while in case of the average roughness an even greater change (210-290%) has been noted. The lastly mentioned changes mean a different class of surface roughness and they may raise the question of serious qualification problems!

Experiences in practice, measurement, evaluation

In technical literature the surface roughness, belonging to a certain tolerance, is given reffering either to Ra or to Rz-value:

Ra= kT n,    (1)

where T is the tolerance, k=0.02; 0.04; 0.08 in case of fine, moderate and rough surface respectively, n=0.8 in all cases,

and Rz = 0.1T (Rz = 0.05T in case of fine, Rz = 0.2T in case of rough finishing),    (2)

or UNI 3963 Italian standard recommendations: Rt=0.25T (rough), Rt=0.125T (fine).    (3)

Considering the fact that the roughness of the surfaces, machined with different machining operations and nearly similar Rz values, achieves the load bearing capacity of 50% in different heights therefore the fitting, considered to be the same, will be significantly different (Fig. 7.).

The expectable development of surfaces, machined with grinding and turning operation  in case of a load bearing of 50%

Figure 7. The expectable development of surfaces, machined with grinding and turning operation in case of a load bearing of 50%

Topological features, resulting by different machining technologies, significantly influence the operation (see Fig. 7.). From it results that – for example, in case of grinding – the load bearing level of 50% – and with this the optimal working surface – can be quickly achieved. So the fitting does not change dramatically during operation or after fitting parts.

Perhaps the most characteristic, but anyway the most known connection of the roughness of working technical surfaces and the measuring process of the machine parts is the case of sliding bearings. Hydrodynamic design of lubricated bearings has been well known and applied in engineering practice for decades. The minimal thickness of lubrication film can be calculated with equation (4), based on the roughness and deformations of shaft and bearing:

h0=(Rt1+Rt2+f1+f2) x    (4)

where Rt1 and Rt2 are maximum roughness values of shaft and bushing (based on the literature “Rt≈4.5Ra in case of machined surfaces”), f1 and f2 are the elastic deformations,

x is the safety factor (in range: 1.2 … 4) [9].

Surface roughness of industrial bearings has been examined by us. Figure 8. shows profiles and some roughness parameters of steel bushing with lining and sintered bronze bushing.

Ra= 3.77 µm, rz= 30.96 µm, rz/ra= 8.21 - profiles of sliding bearings and their roughness parameters. sintered bronze (left), steel with lining (right)

Ra= 3.77 µm, Rz= 30.96 µm, Rz/Ra= 8.21

Ra= 0.19 µm, rz= 1.47 µm, rz/ra= 7.74 - profiles of sliding bearings and their roughness parameters. sintered bronze (left), steel with lining (right)

Ra= 0.19 µm, Rz= 1.47 µm, Rz/Ra= 7.74

Figure 8. Profiles of sliding bearings and their roughness parameters

Sintered bronze (left), steel with lining (right)

Both surfaces – and many other example – demonstrate that the new results of modern tribology have been applied in the industry: the peak zone of surface shows good load bearing properties (high, negative Rsk), volley zone contains deep “craters”, providing adequate lubricant carrying capacity. Rz/Ra value in both cases are higher than 4.5, or even more higher than 7. In case of sliding bearing the cutting or moulding production methods (its application was an everyday practice some decades ago) have been changed by modern technologies. New technologies, providing a better load bearing properties, have been used. At the same time, hydrodynamic theory has not been changed. It means to reach of the optimal operating conditions not only the ratio of Rz/Ra has to be modified, but re-definition of surface parameters is needed from the point of view hydrodynamic theory. Figure 9. shows an example: Although both surfaces have nearly similar average Ra values, the surface, shown on the right side of the diagram, has a significantly higher Rz value, but from the point of view of operation this surface is considered to be better.

Which surface is better…?

Figure 9. Which surface is better….?

It is important to emphasise that the geometric unevenness of surfaces can be characterised by different parameters and not only by the surface roughness (in several cases on the technical drawing there are no information details about them). The deviation from the nominal shape can be correctly characterised with all of these unevennesses. DIN 4760 differ six levels of unevennesses; the most important from these are the form error, the waviness, the roughness and the sub-microroughness. In most of the cases, the form error and roughness are specified in drawings Sub-microroughness (nano-roughness) is in the focus of researches, carried out nowadays, for this reason, the basic principles and their effects are not known yet.

House of climate compressor machined with carbide base material (above) and diamond insert (below). characterisation, based on (p) primary profile containing roughness and waviness as well

Figure 10. House of climate compressor machined with carbide base material (above) and diamond insert (below)

Characterisation, based on (P) primary profile containing roughness and waviness as well

Waviness is a geometric unevenness, influencing significantly the operation of components but it can be found on technical drawings only occasionally [10]. Main cause of it is based on that waviness is “traditionally” momentously lower than roughness so it can be “neglected”. The development of production technology has been driven in order to decrease the roughness but it has not played a considerable role to decrease waviness. For this reason, nowadays the waviness and roughness are in similar range, or waviness values are higher than roughness ones: the potential importance of waviness has been increased. In Figure 10. a sensible example is shown.

Summary, suggestions

If we derive the parameters, to be applied by us, from Ra or Rz values, then the values can vary in a wide range even in case of the same type of application. The generally used connections do not provide appropriate result at all times, therefore it can lead to an unacceptable great mistake.

In an important working case it is advisable to indicate more surface roughness parameters, differing from Ra and Rz. It is influenced by the type of machining as well therefore we have to know how the future working will be affected by the technology, to be applied by us.

The surface roughness in itself does not characterise the microgeometry of working surface, connecting with other surface, as – as a result of filtering – it can differ from the real surface. It requires consideration to use characteristic signs of the primary profile (P), including waviness as well as they can describe the connection of working surfaces in a better way.

The project was realised through the assistance of the European Union, with the co-financing of the European Social Fund, namely: TÁMOP-4.2.1.B-11/2/KMR-2011-0001  "Researches on Critical Infrastructure Protection".

References

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  2. Horváth, S.: A felületi hullámosság 2D-s és 3D-s jellemzése, a működési tulajdonságokra gyakorolt hatásának vizsgálata és elemzése, PhD értekezés, ZMNE – 2008
  3. L. De Chiffre, P. Lonardo, H. Trumpold, D. A. Lucca, G. Goch, C. A. Brown, J. Raja, H. N. Hansen, Quantitative Characterisation of Surface Texture, Annals of CIRP, Vol. 49/2, p 635-652.
  4. Palásti-K, B.: Az érdességi jellemzők információtartalma, Gép, 1992/5. 30-36. p.
  5. Andó Mátyás: Felületi érdesség, Budapest 2010-Gépész Tuning Kft.
  6. Sipos, S. – Biró, Sz. – Tomoga, I.: A termelékenység és a minőség egyidejű növelése WIPER élgeometrival Gépgyártás, XLVI. évf., 2006/4. p. 17-24.
  7. Különféle műanyagok esztergálásakor nyert felületek érdességnek vizsgálata, Kutatási jelentés, Budapest, 2006. Témavezető: Dr. Sipos Sándor
  8. R. Horváth, - Sz. Biró, – S. Sipos: New results in wear mechanisms of PCBN inserts in hard turning, The 6th Int. Scientific Conference Development of Metal Cutting, DMC-2007, Kosice 15-16. 11. 2007. p. 85-90. ISBN 978-80-8073-858-7
  9. Zsáry Á.: Gépelemek II., Nemzeti Tankönyvkiadó, Budapest, 1990.
  10. Horváth, S., - Czifra, Á.: The importance of waviness in study of microtopography of cutting surface, The 5th Int. Scientific Conference Development of Metal Cutting DMC 2005, Kosice, 12-13 September 2005. p.:H 1-4, ISBN 80-8073-303-1

Authors:

1) University Óbuda, Bánki Donát Faculty of Mech. Eng. 1081 Budapest, Népszínház u.8.

palasti@uni-obuda.hu, sipos.sandor@bgk.uni-obuda.hu, czifra.arpad@bgk.uni-obuda.hu

This article was firstly published at the 13th International Conference on Tools (ICT-2012), held in Miskolc (Hungary), on 27-28 March 2012, printed in the official issue of the Proceedings, p. 237 - 244.  (ISBN 978 - 963 - 9988 - 35 - 4)