Surface Roughness

Abstract

Machined surfaces−regardless if they are made of metal, plastic or wood−are never perfectly smooth with protruding parts, valleys and peaks. These forms of surface irregularity are called roughness. Surface roughness can be caused by different factors: discontinuities in the material, various forms of brittle fracture, cavities in the texture (e.g., wood), radius of the tool edge, local deformations deriving from the free cutting mechanism (without counter blade).

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Machined surfaces−regardless if they are made of metal, plastic or wood−are never perfectly smooth with protruding parts, valleys and peaks. These forms of surface irregularity are called roughness. Surface roughness can be caused by different factors: discontinuities in the material, various forms of brittle fracture, cavities in the texture (e.g., wood), radius of the tool edge, local deformations deriving from the free cutting mechanism (without counter blade).

Surface roughness usually has a primary influence on the visual appearance of materials but it might have other effects, too. Surface roughness may be extraordinarily detrimental for wood if the surface under the tool edge suffers permanent deformity. The stability of the damaged surface diminishes to a great extent; the durability of the processed surface will then be inferior.

Visual appearance and colour effects are primarily influenced by dispersion and reflection of light. An apparent example for this is transparent glass, which loses transparency following a moderate roughening process. The original colour of wood becomes a lot more visible if the surface is “bright,” (smooth and free of irregularities). Speaking of wood, a good example is ebony. The black colour gives entirely different effects depending on the surface roughness. The polished surface presents a bright black colour. A surface treated with colourless lacquer, oil or wax will lead to quite different colour effects again.

The minimum surface roughness that can be achieved depends on a number of factors. Generally we can say that processing materials with bigger volume weight can result in smoother surfaces. This explains the excellent polishing ability of ebony.

The surface roughness of wood results from many influencing factors, therefore defining general rules has taken quite a long time [1–3]. Several researchers, trying to overcome the difficulties, used a special filtering method to remove the deep valleys (vessels) from the surface profiles to increase the sensitivity of the roughness parameters to changes in the operational parameters [4–6]. Nevertheless, different wood species hardly could have been compared to one another concerning their surface roughness.

New ideas in the latest decade and modern measurement techniques supported the research works to establish the main governing rules describing the behaviour of different wood species concerning their surface roughness in a unified system [7–12]. In the earlier time it encountered difficulties to characterize wood species and to express their structural properties in terms of numerical values. In order to overcome this problem, it was necessary to elaborate and introduce a new wood structure characterisation method. The newly defined anatomical structure number made it possible to treat all wood species in a unified system facilitating the recognition of general regularities.

8.1 Parameters of Surface Roughness

Machined surfaces always show irregularities of different height and depth that we call “roughness”.

Typical surface roughness profiles for softwood and hardwood species are shown in Fig. 8.1. The first curve demonstrates the surface roughness of Scotch pine of thick growth, where both high and deep irregularities are small. The fourth curve illustrates the machined surface of black locust with large vessels, where the height of irregularities are below 10 μm but the large vessels cause depth irregularities between 50–80 μm.

Fig. 8.1

Surface roughness profiles [8, 12]

It is impossible to find a roughness parameter, which gives an unambiguous characterization of the surface from all aspects; therefore many parameters have been derived, which have been standardized for the purpose of consistent interpretation and usage (Fig. 8.2).

Fig. 8.2

Standardized parameters of surface roughness and waviness

The truly unfiltered profile also contains accidental waviness on the surface. The surface roughness depth P _z can be applied also for this profile, which has a theoretical correlation to the R _z value of the filtered profile as follows:

$$ P_{Z} = R_{Z} + W $$

or

$$ \frac{{P_{Z} }}{{R_{Z} }} = 1 + \frac{W}{{R_{Z} }} $$

(8.1)

In practice maximum roughness profile heights do not necessarily fall on peak heights or valley depths, so the angle of inclination of the straight line described by Eq. (8.1) will be smaller; that is:

$$ {{P_{Z} } \mathord{\left/ {\vphantom {{P_{Z} } {R_{Z} }}} \right. \kern-\nulldelimiterspace} {R_{Z} }} = 1 + {{\alpha W} \mathord{\left/ {\vphantom {{\alpha W} {R_{Z} }}} \right. \kern-\nulldelimiterspace} {R_{Z} }} $$

where the value α is less than 1 (generally 0.6–0.8). The range of the measurement values is shown in Fig. 8.3 [4].

Fig. 8.3

Roughness of the unfiltered profile in relation to waviness based on Eq. (8.1), continuous line = theoretical correlation; area between dashed lines = range of the measured values [4]

A part of the space within the roughness profile is filled with material; the rest of the space is filled with air. The relationship between these two factors is expressed by the material ratio curve of the profile, as in distribution curves. The material ratio curve of the profile is also known as the Abbott curve; its definition and parameters are shown in Fig. 8.4. Modern instruments perform this assessment automatically; the data are drawn and can be printed.

Fig. 8.4

Calculation and characterization of the material ratio curve (Abbott curve) DIN 4776; DIN EN ISO 4287

8.2 The Internal Structure of Wood

One of the typical characteristic features of wood is its internal structure, which has cavities in the form of vessels and cell lumens inside. The typical internal structure of softwood and hardwood species is shown in Fig. 8.5.

Fig. 8.5

Microscopic photo of pine (a) and hardwood (b) species [13]

The early wood tracheids of Scotch pine have large cavities (20–40 μm) and thin walls; however cavities in the late wood are roughly half of the size. The structure of hardwood species is more complicated, consisting of a number of different cell types. Vessels consisting of vertical units doing the transportation; the diameter of which can be up to 300 μm; thus they are visible to the eye. The tracheids, cavities in the long parenchyma cells, are relatively small, in the range 10–20 μm; (see Table 8.1).

Table 8.1 Structural properties of specimens

The cavities of both in the vessels and fibres in the early and late wood are also different in size. Furthermore−depending on the weather circumstances−this variability is typical for the internal structure of subsequent annual rings.

During mechanical processing of wood holes are cut in different angles, therefore even in the case of damage-free cutting (sharp cutting line) hollows do remain on the surface. These valleys cause a certain roughness on the surface, which is not effected by the machining process. Therefore the roughness evolving this way is called structural or structure-caused roughness.

From the aspect of roughness, the internal structure of wood is characterized by the mean diameter of holes and the number of holes in the particular cross-section unit. The size and number of holes has to be determined both in the early and late wood, therefore, the early and late wood ratio must also be established.

In order to gain the above data, small-sized specimens are taken from different wood species, where the required data are established using a measuring microscope or by means of digital image processing. It is practical to check the obtained data also by calculation methods. The bulk density of the sample is easy to determine; the following approximation equation has to be effective (based on a 1 cm³):

$$ \rho_{t} = \left[ {\left( {1 - \frac{{d_{1}^{2} \cdot \pi }}{4} \cdot n_{1} } \right) \cdot a + \left( {1 - \frac{{d_{1}^{2} \cdot \pi }}{4} \cdot n_{1} } \right) \cdot b} \right] \cdot \rho $$

(8.2)

where

• ρ _t , ρ —bulk density and real density of wood,

• d ₁ , d ₂ —mean diameter of cavities in the early and late wood

• n ₁ , n ₂ —number of cavities on the unit surface in the early and late wood

• a, b—ratio of early and late wood (a + b = 1).

We can use the above equation to double-check the early and the late wood separately, knowing that the bulk density of late wood is approximately two times higher than that of early wood.

Table 8.1 summarizes the typical characteristics of the internal structure of samples of conifers and hardwoods [7].

Cutting vessels, tracheids and other elements of the texture causes surface irregularities. We quantified the number of vessels cut on a certain length in the direction of processing. The scattering of the vessel diameters usually shows normal distribution, which enables the utilization of the mean diameter size without making a greater error.

The position of the vessels measured on the surface is always accidental, which obviously causes a scattering of the surface roughness.

Adding up the number of structural elements cut on the surface gives a measure of surface roughness as shown in the model in Fig. 8.6.

Fig. 8.6

The model of structural surface roughness [7]

The area of the valleys has a connection with the number and diameter of structure elements measured along a given unit in the processing direction, which is expressed in the following equation:

$$ \Updelta F = \frac{\pi }{8}\left[ {a.\left( {\sqrt {n_{1} } \cdot d_{1}^{2} + \sqrt {n_{1} } \cdot d_{2}^{2} } \right) + b \cdot \left( {\sqrt {n_{3} } \cdot d_{3}^{2} + \sqrt {n_{4} } \cdot d_{4}^{2} } \right)} \right][{{{\text{cm}}^{ 2} } \mathord{\left/ {\vphantom {{{\text{cm}}^{ 2} } {\text{cm}}}} \right. \kern-\nulldelimiterspace} {\text{cm}}}] $$

(8.3)

where

• n ₁ , n ₂ —the number of vessels and tracheids in the early wood in the unit cross section

• n ₃ , n ₄ —the number of vessels and tracheids in the late wood in the unit cross section

• d ₁ –d ₄ — the diameter of vessels and tracheids in the early and late wood,

• a, b—ratio of early and late wood

The value ΔF defined with the Eq. (8.3) is called structure number, which gives an accurate definition of each wood species based on the size and number of cavities in the wood structure. Surface irregularities caused by the internal wood structure are expected to have a definite correlation with the structure number.

A further advantage of the structure number is that it enables the characterisation of wood species based on their internal structure, and it helps to establish correlations of among the surface roughness parameters.

It is well-known that results of surface roughness tests usually show significant scatterings. One reason is the accidental position of tracheids and vessels on the machined surface. A more significant scattering can be caused by the random position and cut of the early and late wood or the seasonal change of the early wood/late wood ratio. The value ΔF may have substantial differences in the early and late wood. Pine species show the smallest divergence, whereas hardwood species generate a significantly bigger one. Figure 8.7 illustrates the alteration of the ΔF value of different wood species depending on the early wood ratio. The starting point of the curves (a = 0) indicates pure late wood, while the end point (a = 1) indicates pure early wood. Oak shows the biggest change, but ash shows a significant change as well.

Fig. 8.7

Alteration of the ΔF value of different wood species in relation to the early wood ratio [11]

Tests show that the early wood ratio predominantly ranges from a = 0.5–0.7 as shown in Fig. 8.7.

Therefore it seemed practical to apply the relative changes of ΔF in the range a = 0.5–0.7 with the following equation:

$$ \delta \left( {\Updelta F} \right) = \frac{{\Updelta F_{0.7} - \Updelta F_{0.5} }}{{\Updelta F_{0.6} }} $$

(8.4)

Wood species can be characterized with the ratio of cross sections of cavities cut in the early and late wood, which we can express similar to Eq. (8.5) as follows:

$$ B = \frac{{d_{1}^{2} \cdot \sqrt {n_{1} } + d_{2}^{2} \cdot \sqrt {n_{2} } }}{{d_{3}^{2} \cdot \sqrt {n_{3} } + d_{4}^{2} \cdot \sqrt {n_{4} } }} $$

(8.5)

Since pine species lack these vessels, Eq. (8.5) for conifers will be simpler.

Figure 8.8 shows the relative changes of ΔF in relation to the parameter B defined with Eq. (8.5).

Fig. 8.8

Relative changes of ΔF in relation to the parameter B [11]

The apparent correlation between the two variables is clearly displayed. However it is remarkable that beech is located right next to Scotch pine; and black locust shows a smaller relative change than larch.

Consequently the relative change has no connection with the absolute value of ΔF. The correlation follows the following empiric equation:

$$ \delta \left( {\Updelta F} \right) = 7.8 \cdot B^{0.65} [\% ] $$

(8.6)

8.3 The Origin of Surface Roughness

Roughness that evolves during machining has two major components: machining-caused roughness and roughness caused by the internal wood structure. Even in the case of an ideal machining rough surface evolves due to the inner holes cut. Moreover, in the recent practice of high-speed machining, roughness due to machining is usually much less than the structure-based roughness, especially in the case of hardwood species with large vessels.

The roughness due to machining usually depends on the following factors: cutting speed, chip thickness, machining direction relatively to the grain, rake angle of the tool, sharpness of the tool edge (tool edge radius) and vibration amplitude of the work piece.

Wood cutting belongs to the group of the so-called free cutting. Its main characteristic feature is the absence of a counter-edge, therefore, the counterforce is produced by the strength of wood and forces of inertia. The higher strength and hardness parameters (modulus E) the wood has the smaller force of inertia is required; that is to say, the slower the roughness increases with the decrease of the cutting speed.

The primary reason for machining-caused roughness is the brittle fracture of the material and its low tensile strength perpendicular to the grain. The occurrence of brittle fracture cannot be eliminated, however, it can be limited to a lower volume. The most effective method for this is the high-speed cutting and the smallest material contact possible (sharp tool edge).

The only way to eliminate the negative effect of the tensile strength perpendicular to the grain is to generate a compression load in the immediate vicinity of the edge. This can be facilitated with a 65–70° tool angle or a 20–25° rake angle. Especially the edge machining of boards is very inclined to breaking the edge because of the tensile load; therefore the selection of appropriate kinematic conditions is very important (see Fig. 3.12).

Excessive compression load deforming the material can also cause roughness. The method “smooth machining” has been known for a long time, which is based on the knowledge that smaller chip thickness raises smaller forces. Compression load can also be reduced by using the “slide cutting”. Slide cutting produces shear stresses on the edge, which also contributes to material failure. In accordance with the well-known equation the equivalent stress has the following form (see Sect. 2.6):

$$ \sigma_{e} = \sqrt {\sigma^{2} + 4\tau^{2} .} $$

The distribution of compression load under the tool edge depends on its radius (bluntness of the tool edge). Due to the finite thickness of the edge a given layer of thickness z₀ will be compressed underneath the edge (Fig. 8.9).

Fig. 8.9

Compression effect at the edge

The thickness of this layer is about 70 % of the tool edge radius. The load at the edge is transferred onto the material on a surface that is 2b wide and a length that is identical with that of the edge. This is similar to strip load. The biggest load appears just under the contact surface and it rapidly decreases as we move towards the inside of the material (load of the infinite half space). This means that the highest compression of cells always starts directly underneath the edge.

If the compression load underneath the edge reaches the ultimate bearing stress of the material, the cell system suffers permanent deformation and it gets compressed to the detriment of the cavities [14]. If out of total deformation z₀ the permanent deformation is z ₁ , then the expelled material will be located in the lower layers and the thickness of the compressed layer z ₂ is (see Figs. 8.10 and 8.26):

$$ z_{2} = z_{1} \cdot {{\rho_{1} } \mathord{\left/ {\vphantom {{\rho_{1} } {\left( {\rho_{2} - \rho_{1} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\rho_{2} - \rho_{1} } \right)}} $$

(8.7)

Fig. 8.10

Compaction behaviour of early and late wood layers caused by the same blunt edge [14]

where

• ρ ₁ —is the volume density without compression

• ρ ₂ —is the volume density of the compressed material (1–1.2 g/cm³)

The volume density of early and late wood is significantly different, while the value ρ ₂ can change only to a limited extent; therefore we can expect the following values after compression: approximately z ₂  = z ₁ in the early wood and z ₂  ≅ 3z ₁ in the late wood _.

This was also observed experimentally [14]. Figure 8.10 shows the compaction of early and late wood using the same blunt tool. The late wood was compacted several times deeper than the early wood.

If for the purpose of simplicity we presume that the elastic deformation z _r is sustained till the crushing stress σ _B is reached, then:

$$ z_{r} = \frac{{\sigma_{B} 4b\left( {1 - \nu^{2} } \right)}}{E} $$

(8.8)

The deformation underneath the edge is elastic in the first period of the compression so it will rebound once the edge has passed. The approximate rate of elastic deformation can be calculated easily. When the elastic half space is exposed to a strip load:

$$ \sigma = \frac{E}{{2 \cdot (1 - \nu^{2} )}} \cdot \frac{z}{2b} $$

(8.9)

In pine wood, the compression load between directions B and C can have values of σ _B  = 15 N/mm²; then a R = 10 μm radius is likely to produce elastic deformation of approximately z _r  = 1 μm, while a R = 50 μm radius is expected to bring elastic deformation of approximately z _r  = 5 μm. These values give one-seventh of the expected total deformation (z ₀ = 7 and 35 μm,). The compression of the upper layer should be considered in each case.

The wood structure however contains cavities and even cavities of smaller size are comparable to the radius of a sharp tool edge. Therefore the sharp tool edge can penetrate the cavities and break the cell walls. The tool edge bends these broken wood parts, standing out from the cutting plane, which then take the necessary deformation z ₀ without transferring it towards the lower layers (see Fig. 8.26a).

When the tool edge radius is increased, both the edge size and the rate of deformation z ₀ exceed the size of cavities; consequently a compression of the surface layer develops. An approximately R = 20 μm tool edge radius is expected to trigger a surface compression.

In some respect the jointing of an edge has similar effects as edge wear. Jointing is the common practice to produce the same cutting circle for all knives of a cutter head. The jointed land at the edge has a zero degree clearance angle which will compress a thin layer of the wood causing cell damage depending on the jointed land width. This cell damage may be responsible for surface instability, a decrease in gluing strength. It is generally accepted that a narrow band width around 0.25 mm will not create many problems because the area of zero clearance is very small. It is also recommended that the jointed land width should not be more than 1.0 mm.

8.4 The Effects of Machining Process on Surface Roughness

It is well known that a higher cutting speed results in a smoother surface that means smaller roughness values in terms of both the average surface roughness R _a , and depth of irregularities R _z .

Expanding the assessment on the characteristics of the Abbott curve we receive more details concerning the components of the surface roughness (Figs. 8.11 and 8.12). The average diameter of vessels of beech was 60 μm, while for tracheids the corresponding value was 10–15 μm. The mean inner diameter of the tracheids of Scotch pine was 25–30 μm in the early wood and 13–18 μm in the late wood.

Fig. 8.11

Effects of cutting speed on the surface roughness parameters of Scotch pine [7]

Fig. 8.12

Effects of cutting speed on the surface roughness parameters of beech [7]

From Figs. 8.11 and 8.12 in both cases the R _pk and R _k values remain nearly constant or slightly decrease as a function of cutting speed, while R _vk -values depend on cutting speed.

This dependence is stronger with pine, especially at low cutting speeds. This result may be explained by the fact that the pine wood had less local stiffness around the cutting edge, so inertia forces play a more important role to ensure a clear cutting surface. Beech has larger structural cavities, giving greater R _vk -values even at high cutting speeds.

Chip thickness or feed per tooth influences the surface roughness to a smaller extent. This is explained by the fact that the increase of the chip thickness also raises increased forces; and the thicker chip can transmit bigger forces in the connected area at the point where chips are detached.

Figure 8.13 shows the effect of feed per tooth (e _z ) on the irregularity depth (R _z ).

Fig. 8.13

Effects of feed per tooth (e _z ) on irregularity depth (R _z ) 1-oak; 2-beech; 3-Scotch pine [8]

The softer the processed wood is, the bigger is the effect of feed per tooth. The combined parameter of the Abbott curve (R _k  + R _vk ) also shows a good correlation with the feed per tooth, as illustrated in Fig. 8.14. Increasing the feed per tooth also increases the reduced hollow depth ratio R _vk .

Fig. 8.14

Effects of feed per tooth e _z on the combined parameter (R _k  + R _vk ) for Scotch pine v = 50 m/s [8]

The curves in Fig. 8.13 can also be expressed as follows:

$$ R_{Z} = A + B \cdot e_{z}^{n} $$

where A, B and n are constant values. The value of exponent is 0.6 for all of the three curves, and the value of B is almost identical.

8.5 Internal Relationships Between Roughness Parameters

Examining the correlations between the common roughness parameters (average roughness R _a , irregularity depth R _z ) and the Abbott curve we discover some interesting interrelations (Figs. 8.15 and 8.16). Figure 8.15 shows a strong relationship between the average roughness and the sum of Abbott parameters.

Fig. 8.15

Relationship between R _a and the Abbott-parameters [8]

Fig. 8.16

Relationship between irregularity depth R _z and the Abbott-parameters [8]

It is well-known that between R _a and R _z there is only a poor interrelation. As a consequence, no uniquely defined relationship between R _z and the sum of Abbott parameters can be expected. Nevertheless, the experimental results depicted in Fig. 8.16 show an interesting picture.

A lot of curves are obtained. For a more accurate explanation, the measurement results on MDF-boards of different volume density included [8]. MDF has the most uniform internal structure which gives the lowest curve. Oak has large vessels and a much less uniform structure and gives the uppermost curve. The curves for other species are between these two extremes according to their inhomogeneities. Most curves obey the following general form

$$ R_{z} = A.\left( {R_{pk} + R_{k} + R_{vk} } \right)^{0.65} $$

(8.11)

and the constant can be expressed as

$$ A = 7.45 \cdot \left( {R_{k} + R_{vk} } \right)/R_{z} $$

(8.12)

Using the Abbott curve, we can determine the lack of material in the uneven surface. An equivalent layer thickness may be calculated (see Fig. 8.4) as follows

$$ \Updelta h_{e} = R_{pk} \cdot \left( {1 - \frac{{M_{r1} }}{2}} \right) + \frac{{R_{k} }}{2} + \frac{{R_{vk} \cdot \left( {1 - M_{r2} } \right)}}{2} $$

(8.13)

where M _r1 and M _r2 should be substituted as decimal values. The following rough estimation shows the weight of the parts in Eq. (8.13):

$$ \Updelta h_{e} = 0.95 \cdot R_{pk} + 0.5 \cdot R_{k} + 0.08 \cdot R_{vK} $$

(8.14)

In practical cases the R _pk -layer can eventually be neglected because the few peaks sticking out from the surface can easily be crushed by pressing.

A graphic representation of the lack of materials related to the unit surface is seen in Fig. 8.17. The upper curve refers to inclusion of the R _pk -layer. The scattering of measurement data is somewhat higher than in other cases.

Fig. 8.17

Relationship between irregularity depth R _z and the lack of material on the surface with and without the R _pk layer [8]

8.6 The Use of Structure Number

The determination of the structure number ΔF for wood species has become feasible by using the data from Table 8.1 and Eq. (8.3). The structure number gives a unique characterization of a particular wood species concerning its internal structure. Furthermore, differences caused by the area where the tree grew will be taken into consideration. Therefore the structure number is expected to have a definite correlation with the roughness parameters, regardless of the wood species and the area where they were grown.

Samples were processed on a special super surfacer (so-called horizontal surfacer), where the R _Z component of roughness caused by machining did not exceed 10 μm. The relationship established by evaluating 10 different wood species is shown in Fig. 8.18 [7].

Fig. 8.18

Relationship between irregularity depth R _z and the structure number ΔF based on the parameters of 10 wood species [8]

This curve demonstrates the least surface roughness that can be achieved in practice as a function of the structure number. The relationship can be described with the following empiric equation:

$$ R_{z} = 1.22 \cdot \Updelta F^{0.55} $$

(8.15)

To calculate the structure number requires the size and specific number of vessels and tracheids. Additional small specimens to determine the structural properties were cut from each specimen that had been used to measure roughness. Because the structure number is sensitive to the accuracy of experimental data, a combined image processing method and light microscope method was used. The image processing method alone did not generally give results that were accurate enough. The data are summarized in Table 8.1.

To separate the roughness components, three 20 by 5 cm samples were tangentially cut from each wood species. After machining they were finished by a special finishing machine. The finishing was repeated until the profile was flat and suitable for evaluation.

Establishing the finished surfaces, the same samples were subjected to milling operations using various cutting speeds between 10 and 50 m/s. These surfaces were evaluated with the common surface measuring methods.

A hypothetical base line was first established on the finished surfaces. The corresponding R_z’-value was calculated taking only the positive amplitudes into consideration (Fig. 8.19). This is the roughness component due to woodworking operations. Knowing the overall R _z value and subtracting the roughness component due to woodworking, we get to an R _z value due to the internal structure of wood.

Fig. 8.19

Measurement of the roughness component due to machining [9]

Identification the machining roughness enables us to calculate and plot anatomical roughness which is the smallest roughness that can be achieved on a given sample.

Figure 8.20 shows the anatomical roughness and the actual roughness as a function of structure number at two different cutting speeds.

Fig. 8.20

Irregularity depth R _z , related to different cutting speeds in relation to the structure number ΔF 1-cutting speed 10 m/s; 2- cutting speed 50 m/s; 3-anatomical roughness [9]

A general relationship for Fig. 8.20 can be expressed in the following empirical form:

$$ R_{z} = \left( {123\Updelta F^{0,75} + 35e_{z}^{0,6} } \right) \cdot \left( {1 + \frac{{50 - v_{x} }}{50}\frac{0,1183}{{\Updelta F^{0,83} }}} \right) $$

(8.16)

$$ 10\,{m \mathord{\left/ {\vphantom {m s}} \right. \kern-\nulldelimiterspace} s} \le v_{x} \le 50\,{m \mathord{\left/ {\vphantom {m s}} \right. \kern-\nulldelimiterspace} s} $$

where ΔF must be substituted in mm²/cm, e _z in mm, and v _x in m/s. The third part of Eq. (8.16) as well as the curves clearly illustrate that the softer pine wood is more sensitive to a decrease of the cutting speed. This phenomenon can be explained by the lesser local rigidity of pine.

Using a sufficiently high cutting speed, it appeared that the surface roughness will mainly be determined by the internal structure of wood.

In the following we discuss surface roughness parameter ratios which show uniquely defined correlations with the structure number ΔF.

Figure 8.21 illustrates the correlation between the relationship R _a /R _k and the structure number ΔF. The anatomical structure of wood causes a fivefold variation in the R _a /R _k ratios. This leads to the conclusion that wood species cannot be compared on the simple basis of surface roughness.

Fig. 8.21

Correlation between the relationship R _a /R _k and the structure number ΔF [9]

Figure 8.22 shows the correlation between the structure number ΔF and the R _vk /R _z ratio. Here we have a threefold increase in this ratio.

Fig. 8.22

Correlation between the relationship R _vk /R _z and the structure number ΔF [9]

Finally we examined how the core depth of the material ratio curve (R _k ) affects the surface roughness as a function of the structure number ΔF.

Figure 8.23 demonstrates that the value of R _k influences the roughness to a greater extent in soft wood species. It should be noted that the correlation curve in Fig. 8.23 is valid for sharp tools only. The value of R _k is dependent on tool sharpness for all wood species.

Fig. 8.23

Correlation between the relationship R _k /R _z and the structure number ΔF [9]

8.7 Effects of Tool Wear on the Surface Roughness

It is a well-known fact that enhanced wear of the tool increases surface roughness. This is the ultimate practical reason why tools are re-sharpened after a certain working time or cutting length.

Blunt tools with a bigger edge radius transmit bigger forces onto the material causing cell fractures. The material in front of the tool travels a longer distance going around the edge. The forces transmitted to the chip at the detachment point cause a fracture of elementary particles. Fractures beneath the cutting level are primarily expressed in the Abbott parameter R _k . Therefore, this parameter is expected to be highly sensitive to tool edge deterioration.

Figure 8.24 shows the changes in the R _k parameter of four different wood species when using two different tool edge radii.

Fig. 8.24

Changes in the R _k value when using sharp and blunt tool edges in relation to four different wood species [8]

It is clearly visible that the parameter R _k showed a doubling in each case in comparison to cutting with sharp edges. These data show that the parameter R _k gives a good feedback on the deterioration status of the tool edge.

The tool edge radius usually increases the roughness parameter R _z in a linear way. Figure 8.25 illustrates the correlation that was established by testing Scotch pine and beech samples.

Fig. 8.25

Correlation between the parameter R _z and the tool edge radius [8]

We have already mentioned the compressing and destroying effect of a blunt tool edge. The compression of the surface can be observed at an approximately hundredfold microscopic magnification. This phenomenon on a sample of machined Scotch pine is shown in Fig. 8.26 [14]. At the same time, a sharp tool edge cuts a clear surface without compressed layer.

Fig. 8.26

Clear cut of a sharp tool edge (a) and compression of the surface as a result of a blunt tool edge (b) [14]

The permanent deformation reaches the same depth at all places and its depth depends on the quantity of the expelled material (depth z ₀ in Fig. 8.9).

The cell walls get essentially damaged in the compressed layer therefore, this layer loses its stability in all aspect. It will have poor mechanical strength and low abrasion resistance, humidity will cause its swelling to various extents.

Furthermore, an earlier observation has shown that the compressed layer depends also on the chip thickness: using larger chip thicknesses, the same blunt edge exerts more pressure on the bottom layers and the compressed layer increases [15]. This observation further supports the advantage to use small chip thickness for surface finish. The use of oblique cutting may further decrease the damaged layer thickness.

Using a blunt tool edge for machining of large-vessel wood species this may result in surface waviness due to compression. Oak vessels can have diameters up to 250–300 μm; where the edge of a blunt tool can fit in. The edge will not only crumple but also push the material. These motions cause compression and waviness in the upper layer, the majority of the large vessels disappear from the surface due to the compression. Figure 8.27 shows surface profiles of an oak sample cut with blunt and sharp-edged tools.

Fig. 8.27

Surface roughness profiles of oak machined with blunt and sharp-edge tools

When a sharp-edge tool is used, the surface is even; valleys are only caused by cut the vessels and tracheids. Using a blunt tool (R = 53 μm), produces an extraordinarily wavy surface, clogging the majority of the vessels. Consequently, the surface roughness alone is not always sufficient to completely characterize surface quality.

8.8 Scattering of Roughness Data

As it was established in the previous sections, main part of the resultant roughness originates from the internal structure of wood. Cavities in the wood are cut at different angles and positions during machining, which leaves valleys on the surface. The position of the surface is accidental to the position of the vessels, early and late wood. Therefore accidental effects are also present besides effects from deterministic variables which are known. This explains why roughness parameters are always scattered around a mean value. The scattering can be determined with statistical methods using sufficient measurement data.

In order to ensure a normal data distribution, quite many, at least 50 measurements data are required for the statistical evaluation. It is practical to plot the data as a cumulated frequency curve in a probability net, since in this way straight line is achieved. Relevant plotting for Scotch pine and oak is shown in the Figs. 8.28 and 8.29.

Fig. 8.28

Measurement data distribution for a Scotch pine sample [11]

Fig. 8.29

Measurement data scattering of an oak sample [11]

The most part of the curves are straight with a deviation from the straight line only at their ends. This has a simple physical explanation. In practice, unlimited low and high values do not emerge as the theoretical distribution would require. Distributions like this are called uncompleted distribution

The curves clearly display the median (mean) value and the standard deviation: R _z  = 36 ± 4.5 μm in the case of Scotch pine and R _z  = 76 ± 12 μm for oak wood.

Using the curves in Fig. 8.7 we can examine the accidental effects of early wood and late wood. The slope of the curves (∂ΔF/∂a) describes the variability of early wood and late wood, for a given species, which obviously influences their scattering. Figure 8.30 shows the standard deviation of the R _z values in relation to the slope ∂ΔF/∂a for different wood species.

Fig. 8.30

Standard deviation of the roughness parameter R _z as a function of the characteristic number ∂ΔF/∂a for different wood species 1—component due to structural difference in early and late wood, 2—component due to occasional placing of cutting plane to vessels

The curve is not linear but it does not significantly deviate from a straight line. The intersection (σ = ±3.5 μm) that belongs to the value ∂ΔF/∂a = 0 theoretically corresponds with the scattering, due to the accidental position of the surface relative to the vessels and tracheids. The question is whether this value remains constant or not for all wood species. It is very likely not to remain constant; its value will increase in species with large vessels.

The relative value of the standard deviations is worth to examine in relation to the mean R _z value. The test results for different wood species are shown in Table 8.2.

Table 8.2 Values of relative scattering for different wood species

The Table shows that the relative scattering of the surface roughness of different wood species is surprisingly identical, it is dominantly in the range 0.13–0.14. This makes it very easy to estimate the standard deviation.

Finally, the main new recognitions and conclusions on the problems of wood surface roughness can be summarized as follows.

• The total surface roughness can be divided into two component: the first part is the component due to machining and the second part is the component due to internal (anatomical) structure.

• In the present day practice most of the roughness is originated from the roughness component due to internal structure.

• The derived structure number is based on the sizes and specific numbers of vessels and tracheids of the wood in question and further on portion of early and late wood.

• The proposed structure number shows strong correlation with the attainable surface roughness.

• Different roughness parameter ratios show definite correlation with the structure number. This finding further stresses the beneficial use of the structure number uniquely characterizing the different wood species.

• Among the different roughness parameters interrelations are found.

• The lack of material in the rough surface can be expressed as a function of surface roughness.

• The core component of the total roughness R_k is a good indicator to predict edge dullness.

• Using the structural properties of early and late wood, a characteristic number B can be defined which has a strong correlation with the expected relative deviation of the structure number ΔF.

• The standard deviation of the roughness parameter R_z is in strong correlation with the characteristic number $\partial \Updelta F/\partial a$, while the relative value of the standard deviation practically remains constant.

• The standard deviation is originated from both the structural difference in the early and late wood and the occasional placing of cutting plane to vessels.

• An increasing cutting speed reduces the surface roughness, first of all by diminishing the R_vk-values.

• The soft wood species are more sensitive to the change of cutting velocity concerning surface roughness.