1

THE EFFECT OF BELT FINISHING PROCESS VARIABLES ON THE

TOPOGRAPHY OF FINISHED SURFACES

Mezghani Sabeur *, Edoardo Sura °, Mohamed El Mansori *

* Laboratoire de Mécanique et Procédé de Fabrication (LMPF–JE2381), ENSAM –Rue Saint

Dominique, BP 508, 51006, Châlons en Champagne, France.

Sabeur.mezghani@chalons.ensam.fr, mohamed.elmansori@chalons.ensam.fr

° Renault, Direction de la Mécanique/Direction de l’Ingénierie Process – 67, Rue de Bons

Raisins 92508, Rueil Malmaison, France.

edoardo.sura@renault.com

Abstract:

The high performance of industrial applications requires increasingly technical functional

surfaces, particularly from the point of view of topography and micro texture. Belt finishing is

one of the finest machining processes widely used to improve surface texture and to increase

wear resistance and fatigue life. It modifies the surface topography in a wide range of

roughness and waviness scales, and consequently modifies the functionality of the surface in

terms of bearing area, local plasticity and durability. In this paper, the topographic signature

of the belt finishing process on a wide range of wavelengths of surface topography is analysed

to track the effect of each working parameter, and makes it possible then to understand the

principal physical mechanisms activated during the super finishing operations (cutting,

ploughing and friction). To this aim, a multi-scale decomposition of the surface topography

before and after finishing by using a 2D continuous wavelet transform is introduced.

Keywords: Belt finishing, Multiscale decomposition, Surface roughness, Process variables.

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1. Introduction

The technology of super finishing by abrasive belt is remarkably simple and inexpensive. This

process consists to apply a belt on a rotating work piece with a defined pressure and axial

oscillation. During the abrasive tape motion, the abrasive grains undergo an oscillation in a

direction perpendicular with that of the abrasive tape motion (Figure 1).

Figure 1 The general set up of the belt finishing process

Unfortunately, its practical realization is difficult because the basic physical mechanisms of

this abrasion process are still not well understood. So, in the industry, the belt finishing setup

is still based on empirical rules. Indeed, for each new product specification, preliminary tests

are necessary to achieve the optimal operational configuration of a process for a desired set of

outcomes. Moreover, the process variables are numerous and their interactions and effects are

very difficult to evaluate [1] and the effect of each working variable depends on the finishing

operation type (fine or rough belt grinding) [2, 3, 4].

This paper is devoted to the question of how to identify, for a given optimum variable, its

influence on the course of the process and to simultaneously identify the strength of this

influence and its interaction with other working parameters of the process. After defining the

optimum properties of the belt industrial practice, inter-relationships between its

specifications and others working variables (contact pressure, lubrification process and cycle-

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time) which determine tribological processes in the contact area of abrasive belt-workpiece

are investigated.

The concept under consideration is based on the fact that the transfer function of the abrasive

processing system defines the influence of the inputs (i.e. working variables) on the outputs of

the process (i.e. resulted functional surface). So, it is possible to establish a transfer function

by using a multiscale topographic approach to relate inputs and obtained results.

2 Experimental procedure

The research was carried out on materials whose composition and properties are shown in

Table 1 and 2.

Table 1: Parameters of belt finishing process during testing

Material to be finished Input working variables

Composition Steel D38MSV5S with Carbon

content of ~0.35-0.40%

Axial oscillations amplitude (mm) 1

Diameter (mm) 54.8±0.005 Axial oscillations Frequency

(Cycle/min)

150

Axial width (mm) 30 Workpiece rotation speed (rpm) 100

Hardness after heat

treatment, HRC

>50 Average Grits Size (µm)* 9, 15, 30, 40, 80

Table 2: Properties of the used abrasive belt

Studied Abrasive belts Physico-mechanical properties*

Type Microfinishing 372 Kind of abrasive Al2O3

Type of base Polyester

Supplier 3M Band width (mm) 19.84

Average Grits Size (µm) 9, 15, 30, 40, 80

* As specified by 3M.

The signature of belt finishing process was studied under both roughing and finishing of

hardened steel cylinders. The steps involved in their fabrication before belt finishing are:

turning, induction hardening (until a surface hardness higher than 50 HRC) and wheel

grinding with a roughness parameter Ra of 0.9 µm.

The belt grinding was carried out by calibrated of abrasive belt with Al2O3 grits whose size

varies between 9 and 80 µm (cf. Table 1).

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The values of the contact pressure to be investigated were obtained by using shoe-platen

assisted by pressure as described in [1]. Each testing condition was repeated five times and

the obtained results are validated by a statistical analysis (Shapiro-Wilk and Aspin-Welch

tests). Topography features of induced transformations on the finished surface were measured

by a three dimensional white light interferometer (WYKO 3300 NT). The surface was

sampled in 640x480 points with a 1.94μm step scale in the x and y direction.

In this study, first, the effects of the grains size, Abrasivedis studied. After that, for the

determined optimal grains size, the effect of contact pressure, lubrication and finishing

duration variables are studied. The other working conditions and parameters are maintained

constant (see Table 1).

3. Multiscale approach

Various parameters have an impact on the roughness of the finished surfaces: abrasive size,

lubricant, finishing duration, and contact pressure. For that, we need the use of a quantitative

measurement technique regarding all these variables associated to the belt finishing process.

A multiscale analysis approach consisting in the decomposition of topographic surfaces into

different roughness scales has been retained. This decomposition used 2D continuous wavelet

transform. It is applied in order to quantify the manufacturing effect on all the full range of

wavelengths, from roughness to waviness, without any low pass filtering.

The continuous wavelet transform can be interpreted as a multi-channel filter system. The

surface topography components pass through a filter bank which is a set of the contracting

wavelets. The number of wavelets corresponds to the number of iterations.

One defines the 2D wavelet transform of a 2D surface topography f(x, y) by:

,

1( , ) , ( , )

yxb a

x yx y

y bx bW x y f x y dxdy

a aa a (1)

Where ax, ay are respectively the contraction coefficients according to the x and y directions,

bx and by the translation coefficients according to the x and y directions.

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In this study we use the "hat Mexican-2D" wavelet given by the following expression:

)2exp()2(),( rryx (2)

With 22 yxr

It’s an isotropic radial and symmetrical wavelet. It has two vanishing moments and admits

good localization properties at the same time in the space field and the frequencies domain. It

checks well existence conditions of and has a filters band pass behaviours.

The wavelets generated by dilation "a" and the translation "b": , ( , )b a x y are given by:

2 2 2 2

, ( , ) (2 )exp( 2)a b x y x b a y b a x b a y b a (3)

The result of the decomposition makes it possible to identify the component of the surface at

each scale after a 2D inverse wavelet transformation.

The Inverse 2D Continues Wavelet Transform is defined by:

22,, ),(),(1

,yx

yxyx

ba

f

ab

g aa

dadadbdbyxyxW

Cyxf

(4)

With

2

,g

u vC dudv

uv

For Mexican Hat wavelet gC is approximately equal to 3.541

The superposition of all scales of the decomposition creates a cube in (x, y, scale) basis.

(Figure 2)

This approach enables one to analyze the quality of finish performance of the process in a

wide range of wavelength and makes it possible to determine the transfer function of the

process [5 - 7].

The methodology consists of quantifying the arithmetic mean values at each scale of

decomposition. A specter of roughness absolute magnitude “SMa” is obtained (Equation 5).

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*

1 1

( , )( )

fM N

a

x y

W x ySMa a

MN (5)

With * ( , )f

aW x y is the component altitude of the surface “f” at scale “a” in the point

coordinate (x, y). This component is obtained by a 2D wavelets transform. N and M represent

the size of the surface in the x- and y-direction.

Z µm-9.63 5.270

Initial surface Wavelet decomposition

Z µm-6.31 2.37

Finished surface Wavelet decomposition

Figure 2 Example of initial and belt finished surfaces and its decomposition by continuous wavelets

A transfer function of the process that characterizes the roughness attenuation at each scale is

introduced. It’s obtained by determining the ratio of SMa(a) spectrum between the surface

irregularities before and after finishing (Equation 6).

( ) ( )( )

( )

F I

I

SMa a SMa aT a

SMa a (6)

X

X Y

Y

Sca

le

Sca

le

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With ( )ISMa a and ( )FSMa a are respectively the roughness specter of the surface before and

after belt finishing.

As presented in figure 3-b, this computed transfer function identifies the effect of machining

at any scale, and permits quantification of the quality of the surface finishing at defined

wavelength band [6, 7]. As shown in figures 3, the analysis of surface topography with belt

grinding finishing shows a well reduction of the amplitude of roughness [8, 9]. This

attenuation increases the bearing pressure area and reduces the local plastic contact pressures

[10-14].

(a)

(b)

This multi-scale approach was used to define the most appropriate scale of surface

irregularities to be investigated and to consider the effect of the working variable that

contribute to the resulting surface “signature” of the process.

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In the following study, the analysis in the band of wavelength lower than 400µm is

considered. It corresponds to the roughness wavelength band for machined surface

characterization. A fine quantification of the finishing process effect is obtained from micro to

macro roughness scale.

4. Grains size influence

4.1 Characterization parameters

The figures 4 and 5 show the evolution of roughness attenuation from micro to macro

roughness wavelength for various abrasive grains size variant from 9µm to 80µm,

respectively for applied contact pressure of 0.3 and 0.8 MPa.. Two facts are observed:

- A constant attenuation is obtained for abrasive grains size lower than 30µm through

the analysed scale. For abrasive grits size upper than 30µm, the roughness attenuation

increases with scale.

- The maximum attenuation is obtained for 30µm abrasive size.

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The multiscale analysis of the topographic surface before belt-finishing shows the presence of

features with an average length of ~29µm in the machining direction (figure 6). The

characteristic feature length corresponds to the scale of the maximum amplitude of the SMa

specter.

(a) (b)

Then, three cases are distinguished:

When the abrasive grains size is greater than the surface motifs, it can not reach the

small irregularities of the surface. For this raison, the roughness attenuation depends

on scale in this case. The attenuation is more important in macro roughness domain

(from 150 to 400µm);

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When the surface motif’s size and the loads (abrasive grains size) have almost the

same value (≈30µm) a good anchoring is obtained. Adherence is a function of the

mechanical anchoring of the loads in the surface irregularities, then, in this case, the

maximum of adherence between the abrasive grains and surface is obtained and

consequently the high abrasion ability.

For abrasive grains size smaller than the critical value of 30µm, A constant

irregularities attenuation is obtained on all the analysis wavelength range due to the

accessibility of the abrasive grains to the all surface irregularities. However, the

contact area workpiece/abrasive grain is not at its maximum, then, the roughness

attenuation is not optimal.

4.2 Optimal Grain size

The figure 7 shows the evolution of roughness attenuation average with the abrasive grains

size obtained with the application of two different contact pressure (0.3 and 0.8 MPa). It

permits the identification of the optimal abrasive grits size. It is observed for 30µm

corresponding to the highest obtained roughness attenuation. This figure shows also that the

optimal grains size is independent of the applied contact pressure.

5. Comparison between the process variables performances

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To study the effect of the others influent work process variables, the abrasive grains size is

fixed at his optimal value ( Abrasived=30µm).

5.1 Contact pressure and lubrication effect

The figures 8 and 9 show the evolution of roughness attenuation at various scales for some

contact pressure varying from 0.2 to 0.8 MPa respectively in dry and lubricated regime. This

range value of contact pressure is commonly used in the industrial application. A greater

contact pressure will damage the belt stone during the finishing process.

Actually, in dry regime, the contact pressure increases the roughness attenuation (about 4 to 5

% roughness attenuation for each 0.1 MPa contact pressure).

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An important gain of roughness attenuation is observed by adding lubricant during the

machining process (figure 9).

Further, constant roughness attenuation is observed in lubricated finishing regime for pressure

greater than 0.4MPa. Then, from a critical value of 0.4MPa, the using of lubricant neutralizes

the effect of the contact pressure variable.

5.2 Cycle-time effect

The influence of the finishing time duration was studied in lubricated regime for various

applied contact pressure from 0.2 to 0.8 MPa. After 6 seconds, the abrasive band functionality

is reduced. As shown in figure 10, the prolongation of the cycle-time does not influence the

roughness attenuation average. This result confirms the scope of the reference [15] about the

optimal cycle-time in belt finishing.

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6 Conclusions

Optimal grains size for belt grinding is identified by multiscale analysis approach of the

surface before and after finishing. Then, the influences of the process variables of belt

grinding: contact pressure applied by shoe, lubrification condition and finishing duration on

the surface quality of the products, are analyzed using this optimal abrasive grits size.

The use of a multiscale approach allows a fine and stable quantification of the effect of each

process variable on the finished surface quality.

In particular, for contact pressure in the range of 0.2 to 0.8 MPa, the results of this study

specify that for hardened steel component:

- A greater applied contact pressure permits, in dry regime, to ameliorate the surface quality;

- With lubrication, an optimal contact pressure is observed. The use of a greater one not

affects any more the surface quality.

- The prolongation of belt grinding operation after 6 seconds not ameliorates the finished

surface quality.

Furthermore, unlike the abrasive grit size process variable, the contact pressure and the cycle-

time are independent to the roughness scale. The optimal abrasive grits size is then related to

the features length of the original surface.

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7 Acknowledgements

This research has been supported by the Directions Mécanique et Ingénierie Process -

RENAULT (convention CIFRE n°: 769/2004). The authors also thank the partners of this

study: Service Métiers du Process - RENAULT.

8 References

[1] Sura E., El Mansori M., Dal Negro T., Local-pressure control in belt finishing process:

feasability study and experimental validation, Journal of Engineering Manufacture (Part B of

the Proceedings of the Institution of Mechanical Engineers).

[2] El Mansori M., Sura E., Ghidossi P., Dal Negro T., Khanfir H., Deblaise S., Toward

physical description of form and finish performance in dry belt finishing process by a tribo-

energetic approach, Journal of Materials Process Technology. - Article sous presse.

[3] M.C. Shaw, Principles of Abrasive Processing, Oxford Science Publications, Clarendon

Press, Oxford, (1996).

[4] H. Kim, K.M. Marsheck, Belt Forces with Grinding, Journal of Engineering for Industry,

110 (1988) 201-211.

[5] S.H. Lee, H. Zahouani, R. Caterini, TG. Mathia. Morphological Characterization of

Engineered Surfaces by Wavelet Transform. Int. J. Mach. Tools and Manufacturing. Vol. 38,

Nos 5-6. pp. 581-589, 1998

[6] H. Zahouani, S-H. Lee, R. Vargiolu. The Multi-Scale Mathematical Microscopy of

Surface Roughness. Incidence in Tribology. Lubrication at the Frontier. Elsvier Science B.V,

pp 379 - 390, 1999

[7] H. Zahouani, S. Mezghani, R. Vargiolu, M. Dursapt, "Multi-scale study of abrasion

signature by 2D wavelet decomposition", WORLD TRIBOLOGY CONGRESS (WTC-III),

12-16 Septembre, Washington, USA, pp. 839-840, 2005.

15

[8] T.K. Puthanangady, S. Malkin, Experimental investigation of the superfinishing process,

Wear, 185 (1995) 173-182.

[9] A. Jourani, M. Dursapt, H Hamdi, J. Rech, H. Zahouani, Effect of the belt grinding on the

surface texture: Modeling of the contact and abrasive wear, Wear, 259 (2005) 1137-1143.

[10] G. Zambelli, L. Vincent, Matériaux et contact - Une approche tribologique, Presses

polytechniques et universitaires romandes, 1998, pp : 89-97.

[11] G.W. Stochowik, A.W. Botchelar, Engineering Tribology, Butterworth-Heinemann,

2001 (second edition), pp : 483-507.

[12] W. Qu, K. Wang, M.H. Miller, Y. Huang, A. Chandra, Using vibration-assisted grinding

to reduce subsurface damage, Precision Engineering, 24 (2000) 329-337.

[13] D.M. Schibish, U. Friedrich, Technologie de superfinition : Des surfaces de haute

précision, verlag moderne industrie, Supfina Grieshaber.

[14] H. Kim, K.M. Marsheck, M. Naji, Force between an abrasive belt and pulley, Mech.

Mach. Theory, 22-1 (1987) 97-103.

[15] E. Sura, M. El Mansori & al., An energy analysis of belt polishing process and its

applications to time cycle and tracking effects, Machining science and technology, 11,

pp.217-234.

List of figures

Figure 1 (a) Multi-scale roughness Spectrum SMa (b) Roughness attenuation transfer function

Figure 2 Multiscale roughness parameter (work process variables : Pressure 0.3 MPa, with lubrification,

t=12 Sec) for various abrasive grains size

Figure 3 Multiscale roughness parameter (work process variables : Pressure 0.8 MPa, with lubrification,

t=12 Sec) for various abrasive grains size

Figure 4 (a) Surface before belt finishing (b) Extracted profile

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Figure 5 Average Roughness attenuation for various abrasive grains size (9, 15, 30, 40, 80 µm) and two

applied pressure (0.3 and 0.8 MPa)

Figure 6 Multiscale roughness parameter (work process variables : without lubrification, t=12 Sec) for

various applied pressure (from 0.2 MPa to 0.8 MPa)

Figure 7 Multiscale roughness parameter (work process variables : with lubrification, t=12 Sec) for

various applied pressure (from 0.2 MPa to 0.8 MPa)

Figure 8 Average Roughness attenuation for various contact pressure (from 0.2 to 0.8 MPa) for dry and

lubrificant machining process

Figure 9 Average Roughness attenuation at 6sec and 12 sec cycle-time for various contact pressure (from

0.2 to 0.8 MPa)