Effects of debris transfer and abrasive particle damage on the abrasive wear of hardened bearing steel

Wear 247 (2001) 24–32

Effects of debris transfer and abrasive particle damage on the abrasive wear of hardened bearing steel T. Hisakado a,∗ , K. Miura b , H. Suda a a

b

Gunma University, Kiryu, Gunma 376-8515, Japan Hamagumaccom Co. Ltd, Shinurashima, Yokohama, Kanagawa 221-0031, Japan Received 16 August 1999; accepted 2 August 2000

Abstract The influence of the transferred particles on the abrasive paper on the wear rate of the hardened bearing steel (SUJ 2) has been studied using the analytical method, which assumed a conical and a frustum grain without, and with, a transferred particle, and the results compared with the trend of the experimental results. The analytical results revealed that the total cross-sectional area plowed by grains decreased with increasing amounts of transferred particles on the abrasive paper and with decreasing truncated levels of the surface height distribution of abrasives. In the repeated sliding, the transfer of wear particles to the abrasive grains and their shedding occurred so that the specific wear rates of the SUJ 2 pins decreased as presumed by the analytical results. The evaluated method of the specific wear rate was also explained by using the topographical parameters and the fraction of debris removed from the volume of micro-grooves. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Abrasive wear; Analytical method; Transferred particles; Worn abrasive grain; Hardened bearing steel; Topographical analysis

1. Introduction The shape of the abrasive particles in abrasive wear is an important property which largely controls the wear rate. There are three different wear mechanisms observed in single-tip abrasion experiments of ductile materials [1], namely cutting, wedge forming and plowing. Moreover, many experimental and theoretical studies have been performed on the strong coupling between the attack angle and the wear mechanisms for different materials [1–5]. There are, however, also a number of investigations on the effect of other shape properties [6,7,8]. Thus, most investigations are performed with a single abrasive tip performing single pass scratches on flat surfaces. This is removed from the situation in real abrasive and grinding processes, because the abrasive surfaces undergo considerable changes in topography and amounts of wear particles transferred to abrasive grains, etc., as the wear proceeds. The purpose of this paper is to determine the effects of the wear particles transferred to the abrasive grains with their wear, analytically and experimentally. Moreover, when conical abrasive grains were assumed and the fraction α b of debris removed from the volume of micro-grooves plowed ∗ Corresponding author. Tel.: +81-277-30-1570; fax: +81-277-30-1599. E-mail address: [email protected] (T. Hisakado).

by their grains was experimentally obtained against various sliding distances, the wear rates for the hardened bearing steel (SUJ 2) pins with various hardness values could be estimated from the topographical analysis of the worn surfaces [9,10]. The trend of the analytical results also agreed qualitatively with that of the experimental results.

2. Theoretical analysis 2.1. Conical abrasive grain Assuming that a flat surface composed of many conical abrasive grains slides on a soft one and no interference between the plastic deformations of contact points occurs, the dimensionless total cross-sectional area Sp plowed by the conical abrasive grains can be given by [9]   Sp 2 W = tan θ (1) Lx Ly ␲ Lx Ly pf where Lx Ly is the apparent contact area, θ the mean base angle of conical grains, W the normal load, pf the mean flow pressure of a soft flat. The Sp values given by Eq. (1) are independent of both the distributions of the three-dimensional grain summit and two-dimensional surface heights on a profile curves [9].

0043-1648/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 3 - 1 6 4 8 ( 0 0 ) 0 0 4 9 0 - 7

T. Hisakado et al. / Wear 247 (2001) 24–32

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can be given by (u − u0 )2 tan θ  σ  (u − u0 )2 (u − u0 ) + ≡ 2γ tan θ tan θ

Spi = 2a0 (u − u0 ) +

Fig. 1. Shape of a frustum abrasive grain with a transferred particle [a0 ; mean radius of top area on a frustum abrasive grain, at −a0 ; length of transferred particle in the sliding direction, u0 ; separation between a flat and a mean plane of an abrasive paper, and mσ ; maximum height of frustum grain from a mean plane].

2.2. Frustum abrasive grain 2.2.1. Frustum abrasive grain without transferred particle When the tops of conical abrasive grains are worn flat, the shape of grains becomes a frustum one as shown in Fig. 1. The real area of contact Ai for a grain can be expressed as   u − u0 2 σ2 ≡ ␲{γ + (t − t0 )}2 2 (2) Ai = ␲ a0 + tan θ tan θ where a0 is the mean radius of top area on a frustum grain, u an arbitrary distance from the mean plane of abrasive surface, u0 the separation between a flat surface and the mean plane (mean level) of abrasive surface, γ = (tan θ/σ )a0 , σ the standard deviation (rms roughness) of surface height distribution. t = u/σ an arbitrary dimensionless separation, and t0 = u0 /σ . Hence, the number of contact points n(u) are given by Z mσ g(u) n(u) du (3) = Lx Ly ␲{γ + (t − t0 )}2 (σ 2 /tan2 θ) u0 where g(u) is the probability density of surface height distribution, and mσ the height of the highest grain from the mean plane. {f (u) − f (−mσ )} G(−mσ ) G(−mσ ) Z mσ {f (u) − f (−mσ )}du, =

g(u) =

−mσ

1 2 f (u) = √ e−(u/σ ) /2 2σ

(4)

When the separations are given by u = tσ and u0 = t0 σ , g(u) du can be expressed as ( ) 2 2 (e−t /2 − e−m /2 ) 1 dt (5) ϕ(t) dt = √ Φ(−m) 2␲ where 1 Φ(−m) = √ 2␲

Z

m

−m

(e−t

2 /2

− e−m

2 /2

) dt

The cross-sectional area Spi plowed by a grain (see Fig. 1)

(6)

Thus, the dimensionless total cross-sectional area Sp plowed by abrasive grains, can be given by   Z mσ Sp dn(u) = Spi du Lx Ly du u0 Z mσ {2γ (σ/tan θ )(u − u0 ) + (u − u0 )2 /tan θ }g(u) du = ␲{γ σ + (u − u0 )}2 (1/tan2 θ) u0 Z m {2γ (t − t0 ) + (t − t0 )2 }tan θ ϕ(t) dt (7) = ␲{γ + (t − t0 )}2 t0 Assuming that each normal load on a grain is supported on a half front surface of a grain, the dimensionless total real area of contact A/Lx Ly can be expressed as    Z ␲ mσ dn(u) A 1 = {γ σ + (u − u0 )}2 du Lx Ly 2 u0 du tan2 θ Z 1 m ϕ(t) dt (8) ≡ 2 t0 2.2.2. Frustum abrasive grain with transferred particle When the abrasive grains with the transferred particles as shown in Fig. 1 slide on a soft surface, the dimensionless total cross-sectional area Sp /Lx Ly can be given by  Z m   Sp {2γt (t − t0 ) + (t − t0 )2 }ϕ(t) 1 dt = Lx Ly tan θ ␲{γ + (t − t0 )}2 t0 (9) where γ t = (tan θ/σ ) at , at − a0 is the length of transferred particle in the sliding direction, k t = γ t /γ = a t /a0 (see Fig. 1). On the other hand, the dimensionless real area of contact can be expressed as Z 1 m {γt + (t − t0 )}2 ϕ(t) A = dt (10) Lx Ly 2 t0 {γ + (t − t0 )}2 2.2.3. Worn frustum abrasive grain with transferred particle When the frustum grains with the transferred particles are truncated at u = 1σ by wear as shown in Fig. 2, the dimensionless total cross-sectional area Sp /Lx Ly can be given by  Z l   Sp 1 {2γt (t − t0 ) + (t − t0 )}2 ϕ(t) = dt Lx Ly tan θ ␲{γ + (t − t0 )}2 t0 (11) On the other hand, when each normal load is supported on a half front surface of a grain as shown by hatching in Fig. 2,

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T. Hisakado et al. / Wear 247 (2001) 24–32

Fig. 2. Shape of a transferred frustum abrasive grain truncated with wear by mσ −lσ [lσ ; truncated level on a surface height distribution of grains, mσ ; maximum height of frustum grain from a mean plane, u0 ; separation between a flat and a mean plane of an abrasive paper, θ; mean base angle of frustum grain, a0 ; mean radius of top area on a frustum grain without wear, and at −a0 ; length of transferred particle].

the dimensionless total real area of contact A/Lx Ly can be expressed as Z 1 m {γt + (t − t0 )}2 ϕ(t) A = dt (12) Lx Ly 2 t0 {γ + (t − t0 )}2 2.2.4. Wear volume When the wear volume V is in proportion to a sliding distance L and Sp value, the wear volume of a flat surface against an abrasive paper can be given by V = αb Sp L

(13)

where α b is the fraction of debris removed from the volume of micro-grooves plowed. The α b value would be dependent on the penetrating depth, the mean base angle of abrasive grains and the sliding speed.

Fig. 3. Dimensionless cross-sectional area (Sp /Lx Ly )(1/tan θ ) and dimensionless apparent contact pressure W/Lx Ly pf for conical and frustum abrasive grains on the basis of normal distribution of surface heights [k t = γ t /γ = a t /a0 (see Fig. 1), γt = (tan θ/σ )at , γ = (tan θ/σ )a0 , σ ; standard deviation (rms roughness) of surface height distribution].

grain without transferred particles and that with transferred particles. Fig. 4 shows the (Sp /Lx Ly )(1/tan θ ) values for the abrasive paper with the transferred frustum grains truncated at a level lσ by wear. The analyzed results were obtained from Eqs. (11) and (12), assuming m = 5. The figure shows that when the lσ values decrease, the (Sp /Lx Ly )(1/tan θ ) values decrease abruptly and the greater the kt values, the higher is the apparent contact pressure at which the (Sp /Lx Ly )(1/tan θ)

2.3. Trend evaluated from analyzed results Fig. 3 shows the dimensionless total cross-sectional area (Sp /Lx Ly )(1/tan θ) calculated by Eqs. (1), (5), (9) and (10), assuming m = 5 against the dimensionless apparent contact pressure. In this figure, the values for k t = 1 show the calculated results for the frustum abrasive grains without transferred particles. Comparing the calculated values of (Sp /Lx Ly )(1/tan θ) for γ = 0.1,1, and 10 in the case of k t = 1, (Sp /Lx Ly )(1/tanθ) values for γ = 10 are about 0.1 times as large as those for γ = 0.1. The (Sp /Lx Ly )(1/tan θ ) values for γ = 0.1 are 0.8 times as large as those for conical grains. In the range of kt ≥ 2, whose parameters are corresponding to the length of transferred particles in the sliding direction, the larger the transferred particles (kt ≥ 2) and the greater their contact areas supporting the normal load, the smaller are the (Sp /Lx Ly )(1/tan θ) values. This trend of the analyzed results suggests a decrease in the wear rate of pins in the case of the abrasive paper with transferred particles as observed after the repeated sliding in Fig. 4. The values of (Sp /Lx Ly )(1/tan θ) are approximately proportional to the apparent contact pressure for a conical and a frustum

Fig. 4. Dimensionless cross-sectional area (Sp /Lx Ly )(1/tan θ ) and dimensionless apparent contact pressure W/Lx Ly pf for conical abrasive grains without wear and transferred frustum abrasive grains truncated with wear on a level of 1σ as shown in Fig. 2 [k t = γ t /γ = a t /a0 (see Fig. 2), γ t = (tan θ/σ )at , γ = (tan θ/σ )a0 , σ ; standard deviation (rms roughness) of surface height distribution].

T. Hisakado et al. / Wear 247 (2001) 24–32 Table 1 Abrasive papers used in experiment

27

Table 3 Test conditions for bearing steel (SUJ 2) pin

Grain size

Average of grain diameter, d (␮m)

Abrasive material

CC 100 CC 320 CC1000

125 57.3 16.3

SiC

Normal load, W (N) Sliding speed, v (m/s) Sliding distance, L (m)

Virgin surface sliding

Repeated sliding

0.80–2.47 8.25 0.055 0.055 2.97 2.2

0.80–2.47 8.25 0.0681 0.071 122.5–490.1 508

In atmosphere Temperature 20 ± 2◦ C Relative humidity (%RH) 50 ± 5

Table 2 Heat treatments and Viekers hardness of bearing steel (SUJ 2)a pin Vickers hardnessb , HV (Gpa)

Tempering (K)

Density, ρ (×103 kg/m3 )

3.3 5.4 8.9

920 620 No tempering

7.87

a Chemical composition of SUJ 2: C, 0.95–1.10; Si, 0.15–0.35; Mn, <0.50; P, <0.25; S, <0.025; Cr, <1.30–1.60 in wt.%. Hardening temperature; 1130 K (water quenching). b The measuring load was 2.94 N.

values decrease abruptly. Therefore, this suggests that the abrasive paper with the truncated surface height distribution cannot make the cross-sectional area Sp plowed. This figure also shows that the (Sp /Lx Ly )(1/tan θ) values for a frustum grain with γ = 1 and k t = 1 are 0.1–0.4 times as large as those for a conical grain.

3. Experimental procedure 3.1. Virgin surface sliding test with spiral track The properties of abrasive papers (150 mm in diameter) used in a wear test are listed in Table 1. Table 2 shows the heat treatment and Vickers hardness of hardened bearing steel (SUJ 2) pins of 5-mm diameter. The wear tests were performed using a pin-on-disk tester with a spiral track on an abrasive paper, which were stuck on steel disks of 150-mm diameter. After an end surface of each pin had been flattened by repeated sliding on an abrasive paper disk near the center for running-in, a pin was moved in the radial direction of an abrasive paper disk in sliding speed vr of 0.833 mm/s and the average sliding speed was ν = 0.055 m/s under W = 0.80, 1.60, 2.47 and 8.25 N,

so that L = 2.97 m under W = 0.80–2.47 N and L = 2.2 m under W = 8.25 N. The test conditions are shown in Table 3. 3.2. Repeated sliding test with circular track After each pin had been flattened by the same method as in a virgin sliding test, the wear test was carried out on a circular track of an abrasive paper disk. The test conditions are shown in Table 3. 3.3. Measurement of topographical parameters and wear volume The profile curves (measuring length; 5 mm) of wear surfaces on a pin were measured perpendicularly to the sliding direction after removing the pin following each sliding distance of 2.2–2.97 m for the virgin surface sliding, and that of 122.5–508 m for the repeated sliding. About 5000 ordinate data at sampling intervals ∆x = 1 ␮m on each profile curve were put into a personal computer with an analog-to-digital converter in order to analyze the surface topographies. The mean values of θ in Eq. (1) were the averaged values on the profile curves (5 mm of worn surface) measured at sampling intervals ∆x = 1 ␮m perpendicularly to the sliding direction, because the actual slope angles on worn surface could be copied from those of the abrasive grains which plowed in the sliding process (Table 4). The wear volumes of pins for each experiment were obtained from the reduced mass measured by a micro-balance (the minimum scale; 0.01 mg) and the density of material of a pin (see Table 2).

Table 4 Symbols for experimental results HV (GPa)

3.3

Abrasive paper

CC 100

Load (N) 0.80 1.60 2.47 8.25

5.4 CC 320

CC 1000

CC 100

8.9 CC 320

CC 1000

CC 100

CC 320

CC 1000

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T. Hisakado et al. / Wear 247 (2001) 24–32

Fig. 5. Specific wear rate and sliding distance. (a) HV = 3.3 GPa; (b) HV = 5.4 GPa; and (c) HV = 8.9 GPa.

4. Experimental results and discussion 4.1. Specific wear rate and sliding distance It is evident from Fig. 5 that the specific wear rates decreased with an increase in sliding distance L regardless of the normal loads because of increasing transferred particles to the abrasive grains and their wear. Fig. 5(a)

shows that the specific wear rate of HV = 3.3 GPa pin on CC100 abrasive paper decrease little for the sliding distance L = 490–508 m as compared with those on CC320 and CC1000. This is due to the fact that there were a little amount of the particles transferred to the abrasive grains of CC100 as shown in Fig. 6(c) and (e). It is apparent from comparison of Fig. 5(b) and (c) that the harder the pins, the smaller the specific wear rates for L = 490–508 m became

T. Hisakado et al. / Wear 247 (2001) 24–32

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Fig. 6. Scanning electron micrographs of abrasive papers under W = 8.25 N [(a,b) after virgin surface sliding (L = 2.2 m), (c,d,e,f) after repeated sliding (L = 508 m)].

because of the greater particles transferred to the abrasive grains against the harder pins and the wear of their tip areas as appeared in comparison of Fig. 6(e) and (f). These trends of the experimental results agreed qualitatively with those of the analytical results. It is evident from the comparison of Fig. 6(c) with Fig. 6(d) and that of Fig. 7(g) with Fig. 7(h) after the repeated sliding L = 508 m under W = 8.25 N that the harder the pins, the greater is the shedding of the abrasive grains, because the greater amount of CK␣ X-ray in Fig. 7(h) on HV = 8.9 GPa pin than that in Fig. 7(g) on HV = 3.3 GPa pin resulted from the transfer of the bond materials with the shedding of abrasive grains.

4.2. Fraction α b of debris removed from volume of micro-grooves and sliding distance Fig. 8 show the α b values against the sliding distance L. Assuming that the abrasive grains were conical, the α b values were obtained from Eqs. (1) and (13) by using the mean values of θ measured on the profile curves of each worn surface of pins as explained in Section 3.3. It is evident from Fig. 8 that the α b values in the virgin surface sliding were >1, because the pile-up ridges generated by abrasive grains were removed with the rear grains. On the other hand, in repeated sliding the α b values decreased with the sliding

Fig. 7. Scanning electron micrographs and X-ray dot maps of worn surface of bearing steel (SUJ 2) pins after repeated sliding on CC100 abrasive (L = 508 m, W = 8.25 N) [(a, b) SEM image, (c,d) FeK␣ X-ray dot map, (e,f) SiK␣ X-ray dot map, (g,h) CK␣ X-ray dot map].

30

T. Hisakado et al. / Wear 247 (2001) 24–32

Fig. 8. Fraction of debris removed from volume of micro-grooves and sliding distance. (a) HV = 3.3 GPa; (b) HV = 5.4 GPa; and (c) HV = 8.9 GPa.

distance. Although the experimental data are rather scattering, the α b values were independent of the normal load in the range of 0.80–8.25 N. The decrease in the α b values with the sliding distance was attributed to the wear particles transferred to the abrasive grains and the wear of their tip areas as mentioned in Section 4.1. This trend agreed qualitatively with that of the analytical results

as shown in Figs. 3 and 4 indicating the decreasing total cross-sectional area of micro-grooves plowed by the grains. It is evident from Fig. 7(e) and (f) after the repeated sliding L = 508 m under W = 8.25 N that the softer the pins, the greater is the amount of the worn abrasive grains embedded on the pins.

T. Hisakado et al. / Wear 247 (2001) 24–32

Fig. 9. Fraction of debris removed from volume of micro-grooves and Vickers hardness.

It is evident from Fig. 9 that the mean values of α b under W = 8.25 N shown by a dotted line in virgin surface sliding were smaller than those under W = 0.80–2.47 N shown by a dot-dashed line and the harder the pins, the greater are the α b values. The greater α b values for the harder pins suggests that the wear debris generated easily for the harder pins [10], because it was difficult to generate the pile-up ridges in plowing process of the abrasive grains. On the other hand, in the repeated sliding the harder the pins, the smaller are the α b values, regardless of the normal load. This means that the harder the pins, the greater is the amount of the wear particles transferred to the abrasive grains [see Fig. 6(c–f)] and the greater their shedding [see Fig. 7(g and h)], so that the α b values were apt to decrease for the harder pins.

31

Fig. 10. Specific wear rate and fraction of debris removed from volume of micro-grooves.

with decreasing tan θ /pf values in the virgin surface sliding and those decreased with decreasing tan θ /pf values in the repeated sliding except for those of the pins of HV = 8.9 GPa on the CC1000 abrasive paper. The values of tan θ /pf referred to the degree of the surface damage per unit normal load so that, in the virgin surface sliding, the smaller the

4.3. Specific wear rate and fraction α b of debris removed from volume of micro-grooves It can be seen from Fig. 10 that the specific wear rates against the α b values in the repeated sliding can be approximately indicated by a straight line in a log–log scale, regardless of the normal load and the harder the pins, the smaller is the slope of the straight line. This suggests that for the same α b values, the harder the pins, the smaller are the specific wear rates. 4.4. Fraction α b of debris removed from volume of micro-grooves and values of tan θ/pf It is evident from Fig. 11 that although the experimental data were considerably scattered, the α b values increased

Fig. 11. Fraction of debris removed from volume of micro-grooves and tan θ /pf .

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T. Hisakado et al. / Wear 247 (2001) 24–32

measuring the hardness of pins. Moreover, the specific wear rate of the hardened bearing steel pins can be evaluated by using the relationships shown in Figs. 10 and 11. 5. Conclusions

Fig. 12. Mean depth of micro-grooves and tan θ/pf values.

surface damage, the greater are the α b values, and, in the repeated sliding, the reverse trend was found. On the other hand, for the pins of HV = 8.9 GPa on CC1000 abrasive grain in the repeated sliding, the wear particles transferred to the abrasive grains increased tan θ/pf values which resulted from the adhesive and plowing actions with the number of the repeated contact, but the α b values decreased because of the blunt tips of grains. 4.5. Mean depth Sp /b of micro-grooves and values of tan θ /pf It is evident from Fig. 12 that when the values of tan θ /pf for each pin decreased in the repeated sliding, the Sp /bvalues, which indicated the degree of surface damage [11], decreased and the softer the pin, the greater are tan θ /pf values. The relationship between Sp /b and tan θ /pf values could be shown approximately by a straight line in a log–log scale corresponding to the hardness of pins and the grain size of the abrasive paper. Therefore, when the relationship between tan θ/pf and Sp /b values was made clear experimentally as shown in Fig. 12, tan θ /pf values would be able to be evaluated by using Sp /b values without

1. When a conical abrasive grain changed a frustum grain or that with a transferred particle, the total cross-sectional area Sp plowed by the grain decreased. Moreover, when the surface height distribution curve for the abrasive grains was truncated by wear, the total cross-sectional area Sp also decreased. As a result, the specific wear rate decreased. 2. In the repeated sliding, the transfer to the abrasive grains and their shedding occurred so that the specific wear rates of the hardened bearing steel (SUJ 2) pins decreased. This trend agreed qualitatively with that of the analytical results. 3. The fraction α b of debris removed from the volume of the micro-grooves plotted against the specific wear rate of pins could be approximately indicated by a straight line in a log–log scale regardless of the normal load. 4. The mean depth Sp /b of micro-grooves plotted against tan θ /pf values could be approximately indicated by a straight line in a log–log scale and the greater the Sp /b, the greater is tan θ /pf . 5. The specific wear rate of hardened bearing steel (SUJ 2) pin can be evaluated from the relationship between α b values and tan θ /pf , and that between tan θ /pf and Sp /b values on the basis of a hard conical abrasive grain. References [1] [2] [3] [4]

[5] [6] [7] [8] [9] [10] [11]

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