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Effect of the belt grinding on the surface texture: Modeling of the contact and abrasive wear
Wear 259 (2005) 1137–1143
Short communication
Effect of the belt grinding on the surface texture: Modeling of the contact and abrasive wear A. Jourani a,∗ , M. Dursapt a , H. Hamdi a , J. Rech a , H. Zahouani a,b a
Laboratoire de Tribologie et Dynamique des Syst`emes, UMR CNRS 5513, Ecole Nationale d’Ing´enieurs de St Etienne, 58 rue Jean Parot, 42000 St. Etienne, France b Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69131 Ecully cedex, France Received 1 September 2004; received in revised form 31 January 2005; accepted 7 February 2005 Available online 10 May 2005
Abstract Belt grinding is a finishing manufacturing process, which usually follows a hard turning operation. Experimental investigations show that the belt grinding process improves the surface texture and leads to compressive residual stresses. To study the contact between the belt constituted by abrasive grains and the surface, in particular to understand the physical of abrasion, a three-dimensional numerical model is established and presented in this paper. This method provided important and essential information to understand the way the abrasive grains remove the material in the belt and workpiece interface. Important data induced: the normal load distribution, the local coefficient of friction, which depends on the attack angle and then the tangential load on each abrasive grain could be computed. The pressure distribution, the surface deformation and the distribution of real contact area could be also determined by this model. © 2005 Elsevier B.V. All rights reserved. Keywords: Belt grinding; Numerical modeling; Finishing manufacturing; Local coefficients of friction
1. Introduction Hard turning is a finishing operation, which represents a critical and expensive phase of overall production processes. Recent studies [1–3] showed that the surfaces obtained by hard turning are very satisfactory. From a mechanical point of view, this process leads to undesirable residual stress. In fact, this manufacturing technique increases the residual stresses and created hard particles of metal, which can damage the surfaces of the various assembled elements. Moreover, these problems are accompanied by an alteration in the surface texture and metallurgical modifications. To clear up these problems, a superfinishing process must be used. In this work, belt grinding technology is used. Experimental investigations show that the belt grinding process
improves, the surface texture, roughness and material ratio curve. To understand the physics of abrasion and study the effect of the belt grinding on the surface texture, a threedimensional numerical model is established to model the contact between the belt constituted by abrasive grains and the surface. The information provided by this model is: the normal loads distribution, the local coefficient of friction and then the tangential load on each abrasive grain. These contact parameters are of great importance to understanding many tribological situations such as friction, adhesion, wear, thermal and electrical conductance.
2. Experimental procedure 2.1. Belt grinding operation
∗
Corresponding author. Tel.: +33 4774 37588; fax: +33 4774 38499. E-mail addresses: [email protected] (A. Jourani), [email protected] (M. Dursapt), [email protected] (H. Hamdi), [email protected] (H. Zahouani). 0043-1648/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2005.02.113
Fig. 1a and d illustrate a belt grinding operation. The cutting tool consists in geometrically calibrated abrasive grains of silicon carbide adhered to a polymer strip (Fig. 1b and c).
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A. Jourani et al. / Wear 259 (2005) 1137–1143
Fig. 1. Principle of belt grinding (a); belt structure (b); belt SEM picture (c); example of belt grinding device (d).
The belt is applied on the rotating workpiece with a defined pressure and an axial oscillation. The cutting parameters used for these investigations are described in Fig. 2b. This technique removes usually a radial depth of cut of about 4 m, but this value may be included between 2 and 12 m. 2.2. Characterization of belt ground surfaces After the belt grinding operation, analysis was conducted so as to characterize the influence of this process on the surface integrity. The surface topographies, the residual stresses and the metallurgical microstructure have been investigated. A global analyse of the surface topography before and after the belt grinding operation (Fig. 2) reveals that the belt grinding operation has completely deleted the helical surface topography. This new topography is of interest in some applications, such as problems of oiltightness between a spindle and a rubber joint. An observation of two surface roughness profiles (Fig. 3a) shows a decrease in the magnitude of the marks and a great improvement in the Abbott Firestone curve which represents the material ratio of the profile as a function of level (Fig. 3b). Moreover, this process deletes completely the “burrs” obtained on each side of the grooves due the material side flow induced by the hard turning operation. This allows a decrease in the quantity of abrasive particles present in oil. As a consequence the running-in period of the mechanical part, as well as its abrasive wear will be significantly reduced. Additionally, the belt grinding operation tends to improve the reliability of the quality of the cut surface roughness, irrespective of the alteration caused by the wear of c-BN inserts.
To study the effect of the belt grinding on the workpiece, a three-dimensional numerical model is established. This model considers that the local geometry of each abrasive grain is conical and uses the representative strain concept [4] to the determination of the normal and tangential force distribution, the local coefficient of friction, and the real contact area distribution.
3. Conical model of the roughness The indentation by an axisymmetrical indenter allows to estimate the stresses and strains applied in the indented material. For a conical tip geometry [4], the mean pressure is independent of the penetration depth of the indenter, it is only related to the attack angle β of the tip. Following the pressure supported by the summit, we can distinguish three regimes of deformation (Fig. 4). In the case of an elastic contact, the mean pressure undergone by the asperity can be written: pm = 0.2E∗ tan β
(1)
If the contact is elastic–plastic, the mean pressure is given by: E∗ tan β 2 1 + ln (2) pm = 3 3Y where Y is the yield limit and E* is the combined Young’s modulus of two surfaces in contact. When an asperity is deformed plastically, the mean pressure is given by the hardness of the substrate: pm ≈ 3Y ≈ H
(3)
A. Jourani et al. / Wear 259 (2005) 1137–1143
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Fig. 2. Surface topographies obtained (a) after hard turning and before belt grinding (AHT) and (b) after belt grinding (ABG). Cutting conditions in hard turning—tool: TNMG160408 S; cut of speed: 100 m/min; depth of cut: 0.15 mm; feed rate: 0.06 mm/rev. Cutting conditions in belt grinding—abrasive grains: 30 m; rotation speed: rpm; radial depth of cut: 4 m; feed: 0.6 mm/s; oscillation frequency: 12 Hz; oscillation magnitude: ±0.5 mm; force: 170 N; time: 8 s; minimum quantity lubrication with oil.
Recent work shows that a conical geometry of the surface asperities is much more in agreement with the experience [5]. In this present paper, the roughness of the abrasive belt will be modelled by a succession of indenters with a distribution of attack angles β (Fig. 5).
this approach, it is consider the contact between a perfectly smooth plane and the local summits and the interaction between the asperities are totally neglected. If the local area of the contact Aj between an asperity j and the plane is assumed elliptic, having semi-axes aj and bj [6], Aj is given by: Aj = πaj bj
4. Numerical model 4.1. Solution procedure The local behavior of each asperity is investigated numerically by means of the local summits geometry analysis. In
(4)
For a numerical solution, the local area Aj is discretized into N elements cji (i = 1, 2, . . ., N). In this case, the local pressure distribution on each asperity j, is given by the expression: 2 2 1/2 xi 3 yi pj (xi , yi ) = pjm 1 − − (5) 2 aj bj
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A. Jourani et al. / Wear 259 (2005) 1137–1143
Fig. 3. (a and b) Influence of belt grinding on the surface roughness profile and on the Abbott curve.
where pjm is the mean pressure undergone by the asperity j. The normal force Fj exerted on an asperity j is given by the following relation: (6) cji pi Fj = i
The total load supported by summits is: Fj F= j
The contact parameters are computed using the algorithm presented in Fig. 6. The three-dimensional surface topogra-
Fig. 4. Different regimes of deformation.
Fig. 5. Presentation of the roughness summits by cones.
(7)
Fig. 6. The algorithm used to compute the parameters of contact.
A. Jourani et al. / Wear 259 (2005) 1137–1143
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Fig. 7. Topography of abrasive papers.
Fig. 8. Normal loads distribution.
Fig. 9. Distribution of real contact area.
phy is directly sampled by the computer-generated surface topography. For a given initial separation d, the local surface of the contact Aj , the local displacement dj and the average attack angle βj of each asperity can be determined. The distribution of the pressure and the real contact area undergone by the roughness can be then computed. 4.2. Normal loads distribution and real contact area The algorithm is programmed using the Matlab software [7] to study the contact between two abrasive papers defined by their grain sizes (S20 = 20 m; S30 = 30 m) and a smooth
Fig. 10. Conical indenter.
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Fig. 11. Distribution of local friction coefficients.
Fig. 12. Tangential loads distribution.
plane under a nominal contact pressure of 4 MPa. The materials used for two surfaces are Al2 O3 (E = 350 MPa; µ = 0.25). The smooth plane is a steel AISI 1046 (E = 210 MPa; µ = 0.3; H = 1280 MPa). The nominal contact area of two surfaces is Anom = 1024 m × 1024 m, which contains 256 × 256 data points. The topographies of two abrasive belts are shown in Fig. 7. Fig. 8 shows the force distributions computed for two contact problems. The resultant force increases with the increase of the attack angle. The real contact area is much smaller than the nominal contact area Anom (see Fig. 9). It is shown that for different contact surfaces the distribution of the real contact areas is strongly depends on the attack angle distribution of the abrasive belt.
The friction coefficient is independent of the mechanical properties of materials in contact, it is only related to the attack angle β. According to equations (9) and (10), the tangential force Ft is proportional to the grain attack angle and the normal force.
4.3. Tangentiel loads distribution
5. Conclusion
The apparent friction coefficient µ is defined by: µ=
Ft Fn
(8)
where Fn and Ft are, respectively, the normal and tangential force.If the local geometry of each abrasive grain is supposed conical (Fig. 10), the friction coefficient is given by: µ=
2 tan β π
(9)
Ft =
2 tan β Fn π
(10)
Fig. 11 shows the distribution of the friction coefficient using the two abrasive belts. The local normal force and the local friction coefficients allow to determine the tangential loads distribution (see Fig. 12).
The experimental part of this paper shows the technical interest to improve the surface integrity when the belt grinding process in addition to a hard turning operation is used. The surface topography and more particularly, the material ration curve of the profile are improved with both two processes. The geometrical accuracy reached is similar that those obtained using a grinding process. To study the abrasive wear, the heat flux in the abrasive belt and the workpiece interface, it is important to have an idea on the contact pressure, normal and friction forces, local friction
A. Jourani et al. / Wear 259 (2005) 1137–1143
coefficient distribution. To determine these contact parameters, we established the three-dimensional numeric model by modelling the abrasive grains as a distribution of indenters with various attack angles. This model shows there are small real contact areas (approximately, 2% of the nominal contact areas), and the nominal contact pressure is much smaller than the real contact pressure acting over the real contact areas. We can also observe that the local normal and tangential forces increase with the attack angle. From this information, the abrasive wear on each grain could be further determined. The interaction between neighbouring grain and the influence of the grain size and distribution could be also investigated. The contact parameters determined in this paper can be used in our future works to determine: • The local contact temperature distribution due to the heat generation over the real contact areas for sliding problems, which depends on the size of the real contact area, the coefficient of friction, the sliding speed and the thermal material properties.
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• The subsurface stress field, which can give some ideas, for example, about the propagation of the fatigue crack caused in rails by loading due to the rolling wheels.
References [1] H.A. Kishawy, M.A. Elbestawi, Effect of process parameters on material side flow during hard turning, Int. J. Mach. Tools Manuf. 39 (1999) 1017–1030. [2] R. K¨onig, R. Komanduri, H.K. Tonshoff, G. Ackershott, Machining of hard materials, Ann. CIRP 39 (1) (1990) 417–427. [3] J. Rech, Surface integrity in finish hard turning, Int. J. Mach. Tool Manuf. 43 (Iss.) (2001) 543–550. [4] K.L. Johnson, Contact mechanics, in: Normal Contact of Inelastic Solids, Cambridge University Press, 1984, 448 pp. (Chapter 6). [5] A. Jourani, H. Hamdi, M. Dursapt, A. Dellaleau, H. Zahouani, Behaviour elastoplastic of roughness during a static contact between solids, in: Proceedings of the 16th French congress of Mechanics, Nice, September 1–5, 2003, CDROM. [6] J.A. Ogilvy, J. Phys. D Appl. Phys. 24 (1991) 2098–2109. [7] Matlab, User’s Manual, MathWorks, 2001.
Short communication
Effect of the belt grinding on the surface texture: Modeling of the contact and abrasive wear A. Jourani a,∗ , M. Dursapt a , H. Hamdi a , J. Rech a , H. Zahouani a,b a
Laboratoire de Tribologie et Dynamique des Syst`emes, UMR CNRS 5513, Ecole Nationale d’Ing´enieurs de St Etienne, 58 rue Jean Parot, 42000 St. Etienne, France b Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69131 Ecully cedex, France Received 1 September 2004; received in revised form 31 January 2005; accepted 7 February 2005 Available online 10 May 2005
Abstract Belt grinding is a finishing manufacturing process, which usually follows a hard turning operation. Experimental investigations show that the belt grinding process improves the surface texture and leads to compressive residual stresses. To study the contact between the belt constituted by abrasive grains and the surface, in particular to understand the physical of abrasion, a three-dimensional numerical model is established and presented in this paper. This method provided important and essential information to understand the way the abrasive grains remove the material in the belt and workpiece interface. Important data induced: the normal load distribution, the local coefficient of friction, which depends on the attack angle and then the tangential load on each abrasive grain could be computed. The pressure distribution, the surface deformation and the distribution of real contact area could be also determined by this model. © 2005 Elsevier B.V. All rights reserved. Keywords: Belt grinding; Numerical modeling; Finishing manufacturing; Local coefficients of friction
1. Introduction Hard turning is a finishing operation, which represents a critical and expensive phase of overall production processes. Recent studies [1–3] showed that the surfaces obtained by hard turning are very satisfactory. From a mechanical point of view, this process leads to undesirable residual stress. In fact, this manufacturing technique increases the residual stresses and created hard particles of metal, which can damage the surfaces of the various assembled elements. Moreover, these problems are accompanied by an alteration in the surface texture and metallurgical modifications. To clear up these problems, a superfinishing process must be used. In this work, belt grinding technology is used. Experimental investigations show that the belt grinding process
improves, the surface texture, roughness and material ratio curve. To understand the physics of abrasion and study the effect of the belt grinding on the surface texture, a threedimensional numerical model is established to model the contact between the belt constituted by abrasive grains and the surface. The information provided by this model is: the normal loads distribution, the local coefficient of friction and then the tangential load on each abrasive grain. These contact parameters are of great importance to understanding many tribological situations such as friction, adhesion, wear, thermal and electrical conductance.
2. Experimental procedure 2.1. Belt grinding operation
∗
Corresponding author. Tel.: +33 4774 37588; fax: +33 4774 38499. E-mail addresses: [email protected] (A. Jourani), [email protected] (M. Dursapt), [email protected] (H. Hamdi), [email protected] (H. Zahouani). 0043-1648/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2005.02.113
Fig. 1a and d illustrate a belt grinding operation. The cutting tool consists in geometrically calibrated abrasive grains of silicon carbide adhered to a polymer strip (Fig. 1b and c).
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A. Jourani et al. / Wear 259 (2005) 1137–1143
Fig. 1. Principle of belt grinding (a); belt structure (b); belt SEM picture (c); example of belt grinding device (d).
The belt is applied on the rotating workpiece with a defined pressure and an axial oscillation. The cutting parameters used for these investigations are described in Fig. 2b. This technique removes usually a radial depth of cut of about 4 m, but this value may be included between 2 and 12 m. 2.2. Characterization of belt ground surfaces After the belt grinding operation, analysis was conducted so as to characterize the influence of this process on the surface integrity. The surface topographies, the residual stresses and the metallurgical microstructure have been investigated. A global analyse of the surface topography before and after the belt grinding operation (Fig. 2) reveals that the belt grinding operation has completely deleted the helical surface topography. This new topography is of interest in some applications, such as problems of oiltightness between a spindle and a rubber joint. An observation of two surface roughness profiles (Fig. 3a) shows a decrease in the magnitude of the marks and a great improvement in the Abbott Firestone curve which represents the material ratio of the profile as a function of level (Fig. 3b). Moreover, this process deletes completely the “burrs” obtained on each side of the grooves due the material side flow induced by the hard turning operation. This allows a decrease in the quantity of abrasive particles present in oil. As a consequence the running-in period of the mechanical part, as well as its abrasive wear will be significantly reduced. Additionally, the belt grinding operation tends to improve the reliability of the quality of the cut surface roughness, irrespective of the alteration caused by the wear of c-BN inserts.
To study the effect of the belt grinding on the workpiece, a three-dimensional numerical model is established. This model considers that the local geometry of each abrasive grain is conical and uses the representative strain concept [4] to the determination of the normal and tangential force distribution, the local coefficient of friction, and the real contact area distribution.
3. Conical model of the roughness The indentation by an axisymmetrical indenter allows to estimate the stresses and strains applied in the indented material. For a conical tip geometry [4], the mean pressure is independent of the penetration depth of the indenter, it is only related to the attack angle β of the tip. Following the pressure supported by the summit, we can distinguish three regimes of deformation (Fig. 4). In the case of an elastic contact, the mean pressure undergone by the asperity can be written: pm = 0.2E∗ tan β
(1)
If the contact is elastic–plastic, the mean pressure is given by: E∗ tan β 2 1 + ln (2) pm = 3 3Y where Y is the yield limit and E* is the combined Young’s modulus of two surfaces in contact. When an asperity is deformed plastically, the mean pressure is given by the hardness of the substrate: pm ≈ 3Y ≈ H
(3)
A. Jourani et al. / Wear 259 (2005) 1137–1143
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Fig. 2. Surface topographies obtained (a) after hard turning and before belt grinding (AHT) and (b) after belt grinding (ABG). Cutting conditions in hard turning—tool: TNMG160408 S; cut of speed: 100 m/min; depth of cut: 0.15 mm; feed rate: 0.06 mm/rev. Cutting conditions in belt grinding—abrasive grains: 30 m; rotation speed: rpm; radial depth of cut: 4 m; feed: 0.6 mm/s; oscillation frequency: 12 Hz; oscillation magnitude: ±0.5 mm; force: 170 N; time: 8 s; minimum quantity lubrication with oil.
Recent work shows that a conical geometry of the surface asperities is much more in agreement with the experience [5]. In this present paper, the roughness of the abrasive belt will be modelled by a succession of indenters with a distribution of attack angles β (Fig. 5).
this approach, it is consider the contact between a perfectly smooth plane and the local summits and the interaction between the asperities are totally neglected. If the local area of the contact Aj between an asperity j and the plane is assumed elliptic, having semi-axes aj and bj [6], Aj is given by: Aj = πaj bj
4. Numerical model 4.1. Solution procedure The local behavior of each asperity is investigated numerically by means of the local summits geometry analysis. In
(4)
For a numerical solution, the local area Aj is discretized into N elements cji (i = 1, 2, . . ., N). In this case, the local pressure distribution on each asperity j, is given by the expression: 2 2 1/2 xi 3 yi pj (xi , yi ) = pjm 1 − − (5) 2 aj bj
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A. Jourani et al. / Wear 259 (2005) 1137–1143
Fig. 3. (a and b) Influence of belt grinding on the surface roughness profile and on the Abbott curve.
where pjm is the mean pressure undergone by the asperity j. The normal force Fj exerted on an asperity j is given by the following relation: (6) cji pi Fj = i
The total load supported by summits is: Fj F= j
The contact parameters are computed using the algorithm presented in Fig. 6. The three-dimensional surface topogra-
Fig. 4. Different regimes of deformation.
Fig. 5. Presentation of the roughness summits by cones.
(7)
Fig. 6. The algorithm used to compute the parameters of contact.
A. Jourani et al. / Wear 259 (2005) 1137–1143
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Fig. 7. Topography of abrasive papers.
Fig. 8. Normal loads distribution.
Fig. 9. Distribution of real contact area.
phy is directly sampled by the computer-generated surface topography. For a given initial separation d, the local surface of the contact Aj , the local displacement dj and the average attack angle βj of each asperity can be determined. The distribution of the pressure and the real contact area undergone by the roughness can be then computed. 4.2. Normal loads distribution and real contact area The algorithm is programmed using the Matlab software [7] to study the contact between two abrasive papers defined by their grain sizes (S20 = 20 m; S30 = 30 m) and a smooth
Fig. 10. Conical indenter.
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A. Jourani et al. / Wear 259 (2005) 1137–1143
Fig. 11. Distribution of local friction coefficients.
Fig. 12. Tangential loads distribution.
plane under a nominal contact pressure of 4 MPa. The materials used for two surfaces are Al2 O3 (E = 350 MPa; µ = 0.25). The smooth plane is a steel AISI 1046 (E = 210 MPa; µ = 0.3; H = 1280 MPa). The nominal contact area of two surfaces is Anom = 1024 m × 1024 m, which contains 256 × 256 data points. The topographies of two abrasive belts are shown in Fig. 7. Fig. 8 shows the force distributions computed for two contact problems. The resultant force increases with the increase of the attack angle. The real contact area is much smaller than the nominal contact area Anom (see Fig. 9). It is shown that for different contact surfaces the distribution of the real contact areas is strongly depends on the attack angle distribution of the abrasive belt.
The friction coefficient is independent of the mechanical properties of materials in contact, it is only related to the attack angle β. According to equations (9) and (10), the tangential force Ft is proportional to the grain attack angle and the normal force.
4.3. Tangentiel loads distribution
5. Conclusion
The apparent friction coefficient µ is defined by: µ=
Ft Fn
(8)
where Fn and Ft are, respectively, the normal and tangential force.If the local geometry of each abrasive grain is supposed conical (Fig. 10), the friction coefficient is given by: µ=
2 tan β π
(9)
Ft =
2 tan β Fn π
(10)
Fig. 11 shows the distribution of the friction coefficient using the two abrasive belts. The local normal force and the local friction coefficients allow to determine the tangential loads distribution (see Fig. 12).
The experimental part of this paper shows the technical interest to improve the surface integrity when the belt grinding process in addition to a hard turning operation is used. The surface topography and more particularly, the material ration curve of the profile are improved with both two processes. The geometrical accuracy reached is similar that those obtained using a grinding process. To study the abrasive wear, the heat flux in the abrasive belt and the workpiece interface, it is important to have an idea on the contact pressure, normal and friction forces, local friction
A. Jourani et al. / Wear 259 (2005) 1137–1143
coefficient distribution. To determine these contact parameters, we established the three-dimensional numeric model by modelling the abrasive grains as a distribution of indenters with various attack angles. This model shows there are small real contact areas (approximately, 2% of the nominal contact areas), and the nominal contact pressure is much smaller than the real contact pressure acting over the real contact areas. We can also observe that the local normal and tangential forces increase with the attack angle. From this information, the abrasive wear on each grain could be further determined. The interaction between neighbouring grain and the influence of the grain size and distribution could be also investigated. The contact parameters determined in this paper can be used in our future works to determine: • The local contact temperature distribution due to the heat generation over the real contact areas for sliding problems, which depends on the size of the real contact area, the coefficient of friction, the sliding speed and the thermal material properties.
1143
• The subsurface stress field, which can give some ideas, for example, about the propagation of the fatigue crack caused in rails by loading due to the rolling wheels.
References [1] H.A. Kishawy, M.A. Elbestawi, Effect of process parameters on material side flow during hard turning, Int. J. Mach. Tools Manuf. 39 (1999) 1017–1030. [2] R. K¨onig, R. Komanduri, H.K. Tonshoff, G. Ackershott, Machining of hard materials, Ann. CIRP 39 (1) (1990) 417–427. [3] J. Rech, Surface integrity in finish hard turning, Int. J. Mach. Tool Manuf. 43 (Iss.) (2001) 543–550. [4] K.L. Johnson, Contact mechanics, in: Normal Contact of Inelastic Solids, Cambridge University Press, 1984, 448 pp. (Chapter 6). [5] A. Jourani, H. Hamdi, M. Dursapt, A. Dellaleau, H. Zahouani, Behaviour elastoplastic of roughness during a static contact between solids, in: Proceedings of the 16th French congress of Mechanics, Nice, September 1–5, 2003, CDROM. [6] J.A. Ogilvy, J. Phys. D Appl. Phys. 24 (1991) 2098–2109. [7] Matlab, User’s Manual, MathWorks, 2001.