MEASUREMENT SCIENCE REVIEW, Volume 1, Number 1, 2001

MEASUREMENT SCIENCE REVIEW, Volume 1, Number 1, 2001

CUMULATIVE CURVES CHARACTERISING LOAD CARRYING CAPABILITIES AND WEAR PROPERTIES OF SURFACES

Paweł Pawlus, Jerzy Jabłoński

Rzeszów University of Technology

35-959 Rzeszów, ul. W. Pola 2, Poland

fax: +48 17 8543112

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Abstract

The possibilities of generating various cumulative curves were studied. The mutual positions of these curves were analysed basing on computer-generated profiles of various shapes and real profiles of cylinders.

1.  Introduction

Surface topography plays an important role in various functions of many kinds of components. The attempts of contact and wear predictions are based on two kinds of parameters/functions: material/air ratio as the function of height and parameters based on peaks. The material ratio curve was established by Abbott and Firestone [1]. It describes the transition of air to material though the surface profile. It is also a useful tool in characterising a large group of surfaces of some practical importance. These surfaces are not produced in a single operation but in sequence of machining operations [2]. Such processes are termed as multi-process [3] or stratified [4].

Greenwood and Williamson looked for a criterion, which would determine the mode of deformation of an array of asperities of varying heights. Their versions of so-called plasticity index describe the roughness in terms of the mean asperity radius of curvature and the standard deviations of the asperity height distribution [5]. Other workers used different formulae based on a slope [6, 7, and 8]. The conventional way to calculate average peak height is to split the profile vertically into equal height intervals and the count the number of peak within this interval. The peak counts (peak frequency) is sometimes plotted as a function of height, which is called peak distribution histogram. Whitehouse in new paper [9] proposed another method of estimation of peak probability. It does not derive the peak probability curve via the peak count but the “extent” of profile surrounding each peak is measured and summed for each height. In practice each peak is “weighted” by its radius of curvature. This method is called “peak probability”; not “peak frequency”. The proposed curve could be a better indication of the load carrying capability and wear properties of a surface than the material ratio curve and the cumulative peak count, which can give information about spatial correlation of peaks.

2.  The scope of the investigation

In work [9] profile of Gaussian ordinate distribution was analysed. The present authors should confirm the theoretical investigations based on the computer-generated profiles of Gaussian height distribution. Profiles of exponential shape of auto correlation function were analysed. The method of computation originated from paper [10] and adapted from 3D surface topography to 2D profile. Other two curves were analysed: the cumulative HSC curve (high spot count) and average slope cumulative curve. The positions of these 5 curves were compared for irregularity profiles of the same height, defined by Rq parameter, but various correlation lengths CL (the distance at which auto correlation function decays to 0.1). New aspect is the study of computer generated profiles after two processes. The method of this profile generation is described in [11]. Finally, the results of practical experiments were analysed.

3.  Methods

The curvature of a peak [12] is simply expressed by the three-ordinate Lagrangiam differential formula:

y-1,0,+1 are the ordinates of neighbouring points, h is the sampling interval. A point is considered as the peak if his ordinate yo is bigger than ordinates of points y-1, y+1. Each peak was counted (when yo was between y and y +dy) and weighted by the measured value of radius of curvature 1/c. Cumulative probability peak curve was then obtained in a way similar to material ratio curve. Cumulative frequency peak curve was received, when the weighting factors were equal to 1. In addition, the cumulative high spot count curve was analysed. Because the slope is very important factor in contact analyses, the cumulative slope curve was obtained. The local slope [13] was calculated based on the following formula:

dy/dx = (yi+3 –9yi+2 +45yi+1-45yi-1+9yi-2-yi-3)/(60 Dx)

The slope was counted when the point yo was between y and y+dy. The average slope is the mean value of absolute local slopes. The last curve analysed was the material ratio curve MR.

Two-process profile was characterised by the following parameters: Rqp, Rqv, CLp, CLv and plateau depth DIS [14].

4.  Results

Figures 1 and 2 present the cumulative curves for computer-generated profiles of Gaussian ordinate distribution but various correlation lengths. From Fig. 2 one can see that the mutual positions of MR, CPP and CFP curves are the same that Whitehouse suggested [9]. Once correlation length was bigger, CPP and CFP were more similar to each other (the same positions). In Figures 1 and 2 the other curves (HSC and CS) were similar and in the same position to MR curve, but in Fig. 2 distance between these curves and CPP, CFP was smaller.

Fig. 1. Material ratio curve (MR) of Gaussian profile (solid), cumulative probability peak (CPP) curve (points) and cumulative frequency peak (CFP) curve (dashed) - left, cumulative HSC curve (solid), cumulative slope (CS) curve (dashed) – right, CL = 10 mm

Fig. 3 presents computer-generated profiles after two processes. In two profiles Rqp =1 mm, Rqv = 8 mm, distance between fundamental profiles of Gaussian distribution (sometimes called plateau depth [17]) DIS = -5 mm (it means that the mean line of the upper profile is 5 mm below mean line of the lower), but in the upper figure CLv = 10 mm, CLp = 200 mm, in lower figure CLv = 200 mm, CL:p = 10 mm. Figures 4 and 5 present cumulative curves from profiles shown in Fig. 3.

From Figs. 4 and 5 one can see that the functional properties of surface obtained from CPP and CFP curves are better than that obtained from MR curve. CS curve is similar to MR curve to some abscissa (see Fig. 4). In Fig. 5 the cumulative HSC and CS curves are in the same positions.

Fig.2. Similar curves to Fig. 1, but CL = 200 mm

Fig. 3(a) Profile: Rqp = 1 mm, Rqv = 8 mm, CLp = 200 mm, CLv = 10 mm, DIS = -5 mm, (b) profile: Rqp = 1 mm, Rqv = 8 mm, CLp = 10 mm, CLv = 200 mm, DIS = -5 mm

Fig. 4. Various cumulative curves of profile from Fig. 3a

Generally, for two-process texture, HSC and CS curves lie below MR curve, differently to Gaussian profiles. Some real profiles after honing, plateau honing and running in were analysed. For profiles of Gaussian ordinate distribution the positions of MR, CPP, and CFP curves were similar to Withehouse’s prediction. The mutual positions of MR, cumulative HSC and CS curves were rather similar. For stratified profiles HSC and CS curves lie below MR curve, so theoretical prediction was confirmed. For some profiles after running in the analysed curves are similar to Fig.4, which suggests that fine profile can have bigger spacing parameter than base profile. For all the profiles generally, the MR curves were below CPP and CFP curves. Figure 6 presents various cumulative curves for axial profile of plateau honed cylinder.

Fig. 5. Various cumulative curves of profile from Fig. 3b

Fig. 6. Various cumulative curves of axial profile of plateau honed cylinder

5. Conclusions

The possibilities of generating various cumulative curves were studied. In addition to proposal of prof. D.J. Whitehouse other curves: HSC and slope cumulative curves were analysed. For real and computer generated profiles of normal ordinate distribution the positions of these curves was in accordance to Whitehouse’s prediction. For multi-process profiles the mutual positions of these curves is a little different from Gaussian profiles. From the shape of the analysed curve it is possible to obtain more information of functional properties of surface. The next step of investigation will be the analysis of 3D surface topography.

References

1.  E.J. Abbott, F.A. Firestone: Specifying surface quality. Mech. Eng. 1933, 55, 569-725

2.  T.R. Thomas: rough surfaces. Second edition. Imperial College Press, London 1999

3.  D.J. Whitehouse: Assessment of surface finish profiles produced by multi-process manufacture. Proc. Instn. Mech. Engrs., 199, B4, 1985, 263-270

4.  ISO 13565-1,2: 1996: Geometrical product specification (GPS). Surface texture. Profile method: Surfaces having stratified functional properties: Part 1: Filtering and general measurement conditions, Part 2: Height characterisation using the material ratio curve.

5.  J.A. Greenwood, J.B.P. Williamson: Contact of nominally flat surfaces. Proc. Roy. Soc. 1966, 295A, 300-316

6.  B.B. Mikic: Thermal contact conductance: theoretical considerations. Int.J. Heat Mass Transer 1974, 17: 205-224

7.  B.-G. Rosen, R. Ohlsson, T.R.. Thomas; Wear of cylinder bore microtopography. Wear 1996, 198, 271-279

8.  T.R. Thomas, B.-G. Rosen: Determination of the optimum sampling interval for rough contact mechanics. Tribology International 33 (2000), 601-610

9.  D.J. Whitehouse: Some theoretical aspects of surface peak parameters. Precision Engineering, 23 (1999), 94-102

10.  Y.Z. Hu, K. Tonder: Simulation of 3-D random rough surface by 2-D digital filter and Fourier analysis. Int. J. Mach. Tools Manufact. 1992, 32, (1-2), 83-90

11.  J. Jabłoński, P. Pawlus: Computer generation of cylinder surfaces from internal combustion engine. Western Scientific Centre of Ukrainian Transport Academy, No 7/2000, 153-156.

12.  D.J. Whitehouse: The digital measurement of peak parameters on surface profiles. J.Mech.Eng. Sc., IMech, 1978, 20, 221-227

13.  D.G. Chetwynd: Slope measurement in surface texture analysis. J. Mech. Engng, Sc., 1978, 20/3, 115-119

14.  H. Sanna Reddy, J. Raja, K. Chen: Characterisation of surface texture created by multi-process manufacture. Transactions of the 7th International Conference on Metrology and Properties of Engineering Surfaces, 111-118

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