### Introduction

- Top of page
- Summary
- Introduction
- Scope of the Study
- Deep Valleys Analysis
- Results and Discussion
- Conclusions
- References

Cylinder liner texture is a typical example of functional surfaces. Liners have surface topographies with a cross-hatch patterns generated in a finishing process known as honing, and frequently plateau honing. Honing is an abrasive machining process in which material is cut away from the workpiece using abrasive grains which are bound together with an adhesive to form a honing stone. The honing stones are pressed radially while a tool with honing stones vertically strokes and turns, creating a typical cross-hatch pattern. Manufacturers made efforts to find an optimum inner geometrical cylinder structure from internal combustion engine. A plateau-honed cylinder surface, generated in a finishing process ensures simultaneously the sliding properties of a smooth surface and a great ability to maintain oil on a porous surface. It is believed that plateau-honed surface improves the lubrication and reduces friction and wear (Campbell, 1972; Pawlus, 1993, 1994; Jeng, 1996; Johansson *et al*., 2008; Johansson *et al*., 2011).

Plateau-honed surface improving cylinder liner function involves not only tribological tests but also proper characterizing its surface topography in order to better understand changes made in manufacturing process. The importance of areal characterization of surface topography is being increasingly recognized. Plateau honed cylinder liner surface topography provides the example, where the whole areal texture is critical. The angle between honing valleys is very important parameter when producing cylinders because it affects their functional properties (Day *et al*., 1986; Jocsak *et al*., 2006). The specifications of leading engine builders include this parameter and its tolerance. The distribution of these valleys in both directions is also important. For example, the lack of valleys in one direction may cause improper rotation of piston rings. Information about valleys distributions in two directions can be obtained from texture scanning electron microscope (SEM) plots assessed visually or by image analysis (Bayerer, 1994; Bayerer *et al*., 2001). It was found (Papadopoulos *et al*., 2007; Chen and Tian, 2008) that Blechmantel, widths, heights and distances between deep valleys were parameters responsible for a good function of piston ring—cylinder friction pair. To obtain these features, GOETZE (Lenhof and Robota, 1997) suggests the assessment of profiles and SEM images taken from fax-film surface imprints. It is difficult to obtain such parameters from common software. They were achieved by Bayerer *et al*. (2001), Dimkovski (2011), and Anderberg *et al*. (2006).

Different methods can be used to characterize the directionality of machined surfaces, including spectral moments (Nayak, 1971), structure function (Sayles and Thomas, 1977), cross-correlation function (Tanimura *et al*., 1982; Boudreau and Raja, 1992) as well as areal autocorrelation and power spectral density functions (Stout *et al*., 1993; Dong *et al*., 1994). Other applications of cross-correlation technique are described by Condeco *et al*. (2001) and Vorburger *et al*. (2011). Cross-correlation function can be used to characterize surface directionality when the nominal lay direction is not perpendicular to the profile direction (Tanimura *et al*., 1982). But this method is less effective for complex surface and small degree of directionality (Boudreau and Raja, 1992). Instead, power spectral density function is recommended (Boudreau and Raja, 1992; Dimkovski, 2011). Hough transform was used to find the central grooves (valleys; Dimkovski, 2011). An angular spectrum plots an amplitude or power in a line on the surface against the direction of that line. In work (Pawlus and Chetwynd, 1996a) the usefulness of cross-correlation, autocorrelation, and power spectral density functions in the analysis of the directionality of cylinder liners surface topography was studied. The lay angles were estimated correctly by angular spectra derived from cross-correlation functions and areal power spectral analysis, while their variation was the best using the cross-correlation function. Cross-correlation function application requires smaller computing time and fewer profiles than power spectral analysis and was better in analyzing surfaces with complicated structure (honed surface after a low wear process). Analysis via autocorrelation function was not recommended because it gave no obvious advantage over the other methods and involved intense computation.

### Deep Valleys Analysis

- Top of page
- Summary
- Introduction
- Scope of the Study
- Deep Valleys Analysis
- Results and Discussion
- Conclusions
- References

Figure 1 shows the orientation of valleys directions. *β* angle is determined in angular spectrum, *α* is the honing angle.

The fundamental idea of the proposed approach is that the ratio between the widths of deep honing valleys measured in two perpendicular directions VW_{y}/VW_{x,} should equal tan(*β*) (see Fig. 2). Method based on this idea was used previously (Pawlus and Chetwynd, 1996a), but the former approach did not lead to proper determination of the major angles. The main directions obtained previously were often smaller (0°–90° quadrant) and larger (90°–180° quadrant) than the correct values. The reason of it was that in previous procedure a valley bottom was recognized as a point of lower ordinate than those from four adjacent points (similar to commonly used definition of summit). In new algorithm the surface point was considered as probable valley bottom if its ordinate was smaller than ordinates of two neighboring points from each side in the analyzed directions (x and y). This is the first difference between procedure used in this paper and in Pawlus and Chetwynd (1996a). The second difference is method of deep valley identification. Previously (Pawlus and Chetwynd, 1996a), a valley was determined as deep if its bottom was below the point of maximum curvature of the normalized material ratio curve. In new procedure, the deep valley was recognized on the basis of the Sk parameters group (areal version of ISO 13565-2 standard). New procedure of valley recognition is easier than previously used method. Furthermore, the deep valleys analysis can be done automatically. There were also other differences between these two approaches.

The real valley width is smaller than value obtained from the analysis of profile in x-direction: VW = VW_{x} sin(*β*)—see Figure 2.

The valley was recognized as deep if its bottom was below the ordinate yr2 of point of abscissa Sr2 (see Fig. 3). Total depth (height) should be larger than a critical value related to the Svk parameter. It was found after the analysis of various honed cylinder surfaces that the depth of the valley should be higher than 0.5 Svk; in this case the average valley depth is close to Svk. Of course this condition can be changed if the resultant mean valley depth was considerably different than Svk.

First, for all the rows (profiles) in x-direction the bottoms of deep valleys were identified. When bottom of each valley was below yr2 point, its edges in two perpendicular directions x and y were searched. Figure 4 presents an idea of edges identification in one direction. The edges E1 and E2 were identified if their ordinates were higher than ordinates of possible deep valley's bottom and higher than those from adjacent points.

Next for the found edges the height differences between edges and valleys bottom was computed, and valley was identified when these differences for all four edges were higher than critical value, say 0.5 Svk. When the valley was identified, the angle *β* was computed from the ratio of valley widths in perpendicular directions, being its tangent. However, the tangent does not discriminate between the two lay directions. To do this and to avoid intersection points of two valleys, for which widths ratio can be incorrect, the heights of ordinates were summed in the possible lay directions and the angle was counted only if these heights were significantly smaller in one direction than in the other (see Fig. 5). For example, it was found that this angle was counted correctly if sum of ordinates of points P1, P2, P3, and P4 was smaller than sum of P5, P6, P7, and P8 by at least 4 Svk (of course this condition can be changed for different cylinder textures). In Figure 5, *β* angle is smaller than 90°.

It is necessary to note that all the found widths of the valleys were counted, but only some of them were analyzed for determining the angular spectra.

After finishing calculation of each row in x-direction the distance between deep valleys were counted. Then the similar calculation was done for each column in y-direction. The resultant valley height in each direction was the smaller height from both valley sides.

The main output from this software was angular spectrum. It was obtained by three ways:

- plotting the sum of heights VH of all deep valleys indicating a particular angle;
- plotting the sum of product of height VH and widths VW (see Fig. 2) of deep valleys; and
- plotting the counts of deep valleys.

In the second method, the weight is related to valley oil capacity.

In addition, distribution of valleys widths and heights as well as distances between the deep valleys in perpendicular directions were given. All the points of valleys were computed, so these valleys can be recognized in surface contour plots. Figure 6 shows flow chart of the algorithm (m is the number of rows, n is the number of columns).

### Results and Discussion

- Top of page
- Summary
- Introduction
- Scope of the Study
- Deep Valleys Analysis
- Results and Discussion
- Conclusions
- References

To test the algorithms, surfaces having simulated valleys of triangular shape were used. These valleys of various angles *β* were imposed on measured or simulated isotropic surfaces of standard deviations of height Sq between 0.3 and 1.1 µm. All of the methods determined the main directionality correctly. Figure 7 shows example of surface characterized by the Sq parameter of 0.6 µm and the level of isotropy of 0.6 (texture-aspect ratio Str parameter) with additional valley of about 35 µm depth. Because the valley occupied only small area, the critical (minimum) valley depth was calculated based on the profile analysis.

The main sequence of tests used the real surfaces. About 20 plateau honed cylinder surfaces were analyzed. Similar information about main directionality in two directions was obtained using three methods. Cross-correlation method gives the smallest variation of the honing angle. It is probably good for assessing deviations of honing angle. For all the pairs of profiles only the main direction is identified by this method. Please note that in calculation using cross-correlation function the obtained angles were weighted by the associated value of the cross-correlation. The results of cross-correlation function application seem to be only affected by deep valleys presence when no other special features exist on the surface. However, in angular spectra obtained from power spectral density function the background structure is also taken into consideration. Cross-correlation method and deep valley analysis cannot be applied if main lay direction is perpendicular or orthogonal to measurement directions, contrary to method based on power spectra. Deep valleys analysis method describes correctly the main angles in two directions, but it shows also smaller values of angle in the range 0°–90° and higher in the range 90°–180° than the other methods. It is caused by the ratios between valleys widths in two perpendicular directions. Usually in angular spectrum the directionality angles of 45° and 135° are determined. However, the main advantage of this method is that information about features specific for honed cylinder liners (distributions of valleys widths, heights and distance between them) can be obtained. Power spectral density method and then deep valleys analysis are good in determining third and fourth directions as the result of imperfect honing, it can be hard to recognize these directions using the cross-correlation approach.

As mentioned above, three possibilities of weighting angle in deep valleys analysis method were considered. It is difficult to say what approach is the best. The present authors selected method depending on plotting the sum of heights of all deep valleys indicating a particular angle. After application of this approach the ratio of the largest values (modes) in each quadrant was the most similar to that obtained using cross-correlation method, when angles were weighted by the associated peak value of the cross-correlation (square of height)? These values were similar to those obtained by direct assessment. However, in some situations (e.g., the analysis of potential lubrication), the angle should be weighted by the product of valleys width and depth, indicating the oil capacity. When the distance between deep valleys is important, the method based on deep valleys counting should be recommended.

Surfaces A and B were measured by stylus equipment Talyscan 150 with nominal radius of tip of 2 µm. Figure 8 presents surface A and angular spectra obtained by various methods, with three approaches of the deep valley identification. One can see that when angle was weighted by product of valley width and height the importance of 45° angle is similar to the main directionality in the quadrant 0°–90°.

It is widely known that sampling interval has a significant influence on spatial parameters of honed cylinders surface topography (Dong *et al*., 1996; Pawlus and Chetwynd, 1996b). Therefore additional experiments were performed to study the sensitivity of deep valleys analysis method on sampling interval. Increased sampling interval can diminish background noise, except when it becomes too large to resolve the structure. For too small sampling interval, it can be difficult to correctly determine valley dimensions and then honing angle. Some small structures can lead to underestimate the deep valleys depth. As a consequence, the number of identified valleys would be too small. For too large sampling interval also the number of deep valleys would be too small. After the analysis of a lot of surfaces measured both by stylus and optical methods it was found that sampling interval, for which the minimum (smallest) distance between deep valleys was obtained, should be selected. The following procedure is proposed: measure cylinder liner surface topography with small sampling interval, for the same measured area increase sampling interval, in each case determine deep valleys parameters and select sampling interval for which the distance between deep valleys is the lowest. After that, the surface can be re-measured for a larger measured area with the proposed sampling interval.

As said, information of features specific for honed cylinder liners can be obtained by deep valleys analysis application. Figure 9 plots contour map of surface B with angular spectra computed by cross-correlation, deep valley analysis (weighted only by the valley height), and power spectral analysis.

In order to obtain numerical comparison, the analyzed methods were compared using several parameters calculated from the angular spectra to describe the valleys directions and variability: the mean value of each quadrant, the mode (largest value) in each quadrant, standard deviation in the quadrant (std), the ratio of the sums of the vertical values of the two quadrant (rs), and the ratio of the modal values (rm). Table I gives these parameters for surface shown in Figure 9.

Table I. Results of texture directionality measurement for cylinder surface shown in Figure 9Parameters | Cross | Cross | Deep valleys | Deep valleys | Spectrum | Spectrum |
---|

0°–90° | 90°–180° | 0°–90° | 90°–180° | 0°–90° | 90°–180° |
---|

Std, ° | 3.98 | 7.05 | 6.75 | 6.76 | 13.97 | 17.77 |

Mean, ° | 65 | 115 | 60 | 124 | 63 | 123 |

Mode, ° | 64 | 118 | 64 | 118 | 65 | 118 |

rs | 1.12 | 1 | 2.66 | 1 | 2.4 | 1 |

rm | 1.9 | 1 | 3.49 | 1 | 2.16 | 1 |

Values of parameters std, rs, and rm are the main differences among the results presented in Table I for three different methods of surface directionality assessment. It is evident that cross-correlation method gives the smallest standard deviation while the power spectral method gives the largest. The highest standard deviation of main directions obtained by power spectral analysis was caused by background noise consideration. Deviation of honing angle is larger using this method for angles 90^{o}–180^{o}, contrary to results of deep valleys method application, in which the std parameter is similar in both angular directions. After visual assessment it seemed that deviation of honing angle in two directions was similar. True direction is represented better by the modes than the means. The mode values were nearly the same using three analyzed methods. The mean and mode values were similar from cross-correlation method application, but analysis based on spectra and valley widths gave means different from modes. The angle distribution is consistent after using three analyzed methods. Similar values of rs parameters were obtained after application of deep valleys analysis and power spectral method; cross-correlation approach gives the smallest value. From direct analysis of surface contour graph it is evident that honing valleys are not evenly distributed. However, the rm parameter is the highest after using deep valleys approach, but applications of the other methods assured smaller ratios.

With the presented system of deep valleys identification it is possible also to obtain distributions of valleys widths, depths, and distances between them. The identification of the bottoms of the valleys is the first step to deep valleys recognition. Figure 10 presents distribution of valleys widths and depths in x-direction of surface B shown in Figure 9. Valleys depths and widths are presented for each identified bottoms of valleys. The distances between deep valleys are shown for various profiles in y-direction. Selected sampling interval in deep valleys analysis was 10 µm. The mean valley height in x-direction was 2.83 µm, the mean valleys width in x-direction was 65.9 µm, the mean distance between deep valleys in x-direction was 211.6 µm, in y-direction (not shown in graph) was 351.7 µm. The application of developed software allows to analyze valleys of various heights; the parameter yr2 (see Fig. 3) and minimum height of deep valley can be changed.

Figure 11 presents horizontal coordinates of all the found bottoms of deep valleys from surface shown in Figure 9. Because all the valleys bottoms are presented in Figure 11, therefore some points not belonging to deep valleys could be identified. The deep valleys could be better recognized when only their bottoms used in angular spectrum graph would be presented. A more in-depth research in this direction is required in future work.

Deep valleys analysis gave different information than the other methods. It characterizes only deep valleys but method based on the power spectra describes also about plateau part of the surface. However, the application of power spectral analysis and cross correlation functions do not present information about distribution of valleys sizes and distance between valleys, it is not possible to identify deep valleys using these approaches. Deep valley analysis is slower than other methods studied, but computation time is not too high.