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Fretting wear of thin steel wires. Part 2: Influence of crossing angle
Wear 273 (2011) 60–69
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Fretting wear of thin steel wires. Part 2: Influence of crossing angle A. Cruzado a,∗ , M. Hartelt b , R. Wäsche b , M.A. Urchegui c , X. Gómez a a
Mondragon Goi Eskola Politeknikoa, Mondragon Unibertsitatea, Loramendi 4, 20500 Arrasate-Mondragon, Spain BAM Federal Institute for Materials Research and Testing, Unter den Eichen 44–46, D-12203 Berlin, Germany c ORONA eic, Polígono Industrial Lastaola s/n, 20120 Hernani, Spain b
a r t i c l e
i n f o
Article history: Received 2 September 2010 Received in revised form 11 April 2011 Accepted 21 April 2011 Available online 17 June 2011 Keywords: Fretting Wires Contact pressure Crossing angle
a b s t r a c t The wear behaviour of thin steel wires has been analyzed under oscillating sliding conditions in crossed cylinders contact geometry. The focus of this analysis was the influence of the crossing angle between the wires on the wear. The wires used had 0.45 mm in diameter and the material was cold-drawn eutectoid carbon steel (0.8% C) with a tensile strength higher than 2800 MPa. Two different types of tests were carried out, the first one representing the influence of the crossing angle for a constant load and the second one representing the influence of the crossing angle with constant contact pressure. In the first type of tests it was seen that as the contact angle decreases the contact pressure decreases too and hence less energy specific wear resistance is observed. As a consequence less wear is produced, thus increasing the life of the wires. In the second type of tests it was seen that with constant contact pressure but different crossing angles, nearly the same energy specific wear resistance was observed. This points at an identical wear behaviour in both type of tests but with a running-in and a steady state period as two different wear periods. The tests showed that the running in period may play an important role in the overall wear particle generation and hence the wear occurring in the steady state period is rather mild. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Steel wires in form of thin wires are used to construct wire ropes being used in many industrial applications, like structural elements (reinforcement for tires, bridges, barges etc.) or as elements for transporting purposes (cranes, lifts, funicular railway, ski lifts) due to their high axial strength and bending flexibility. These mechanical properties of the ropes are largely dependent on their construction and the properties of the wires itself, because the wires are wound into strands, which are then wound to form the rope (Fig. 1). The properties of the rope depend on the number, size and arrangement of the wires in the strands, the number and arrangement of the strands and the core type. Despite their outstanding mechanical properties steel wire ropes are prone to degradation due to fretting damage [1]. If tensile loads are applied and/or released, or the rope runs over a sheave, the contact pressures between wires change and oscillatory motions between the contacting wires occur. Due to the bending when the ropes run over the sheaves, the stress in the contact area is largely increasing. Under the oscillatory motion between the wires this leads to increased wear [2,3] and subsequently producing the failure of the rope. The effect of fretting wear is especially important in point con-
∗ Corresponding author. Tel.: +34 943 73 96 92; fax: +34 943 79 15 36. E-mail address: [email protected] (A. Cruzado). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.04.012
tacts (typically between the outermost wires of strands and core or between the outermost wires of adjacent strands). Since the wear is directly dependent on the bending of the rope, until now the radius of the sheave had to be large so that security tolerance was large enough to avoid catastrophic failure of the rope during the operating time period. Under compulsion of smaller space for elevating units lift manufacturers want to use smaller sheaves with the aim of reducing the dimensions of the electric motor. Smaller sheave diameters lead to higher bending of the rope and consequently to a higher wear of the wires and a considerable decrease of the fatigue lifetime of the ropes [4]. For further understanding of rope degradation mechanisms it is important to analyze the wear mechanisms occurring in the different parts of the rope during service. Since fretting wear reduces the diameter of the wires, it is one of the main reasons for a shortened life time of a wire and therefore adds an important contribution to the degradation of the rope of this type of wires in fretting conditions dependant on different parameters like sliding length, frequency and contact pressure. Urchegui [5] analyzed fretting wear of thin steel wires using different operational variables like normal force, stroke and number of cycles. This investigation was continued with a widened parameter field [6] mainly with an extension to the parameters normal load and loading time (number of cycles). In both cases, the crossing angle was 90◦ . The main conclusion was that the wires are submitted to two distinctive behaviours: one corresponds to the
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Fig. 1. Schematic of a wire rope composed of different strands of wound steel filaments.
running-in period, with a more aggressive wear behaviour, and the second one corresponds to the stable period with mild wear behaviour. However, both are in close relation with the contact pressure. In this paper with the aim of representing a more realistic wire contact configuration, different tests with different crossing angles were performed. Taking into account the influence of the contact pressure in the wear behaviour two types of tests were performed: the first one corresponds to maintaining the same load for different crossing angles, so that the mean contact pressure changes during the test due to wear and the second type of test is aimed at maintaining the same mean contact pressure for different crossing angles. However, the mean contact pressure can only be known in the beginning of the test, not during the ongoing test with time. This influence therefore has not been studied. 2. Experimental details 2.1. Tribological testing For tribological testing the contact geometry of crossed cylinders was used to simulate the fretting wear behaviour of the wires in ropes. This method allows for an exact determination of wear under the required conditions [5,7]. The wires used for the experiments are wires which are usually fabricated into a 7 × 19 rope (7 strands with 19 individual wires in each one). The diameters of the wires are different and range from 0.22 mm to 0.45 mm (Fig. 1). For the tests, wires with a diameter of 0.45 mm, were used. They are cold-drawn from eutectoid carbon steel with 0.8% C with a tensile strength greater than 2800 MPa and a hardness of 659 ± 81 HV 0.05. The surface average roughness (Ra ) of these wires along its axis was 0.35 and 0.70 m in perpendicular direction. These values were obtained from the measurements carried out at an unworn wire using a confocal imaging profiler (Pl, Sensofar). The wires are usually covered with a thin film of brass with a film thickness of less than 1 m (Fig. 2), of which the exact composition is unknown. The chemical composition of the film brass was qualitatively analyzed by energy dispersive X-ray microanalysis (EDS) in the scanning electron microscope (SEM), in which peaks of Cu and Zn, typical chemical elements of the brass, were observed. Fretting wear tests were carried out on a tribometer which is described in more detail in [6,8]. During each test the real stroke (xreal ), friction force (Ff ) and total linear wear (Wl,tot ) were measured. Relative humidity (RH) and temperature (T) were kept constant during the test. All measured quantities were recorded
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Fig. 2. SEM micrograph of Brass film cover in a longitudinal cut of the wire.
on-line multiple times. After each test friction and wear quantities are derived from the stored values. The planimetric wear (Wq ) and the volumetric wear (Wv ) subsequently determined from wear scar profilometry (Hommeltester, Fa. Hommel, Homburg, Germany) as described in detail by Wäsche and Hartelt [7]. 2.2. Test program Based on an analysis in an earlier study it was known that in a new unused rope plastic deformation appeared. Therefore in these tests the value of average contact pressure was chosen to be higher or lower than the yield strength of the wires (2800 MPa). Furthermore the selection of the oscillating amplitude was done based on a simulation study. In this study a real situation was simulated with a rope running over a sheave of 200 mm diameter. Under these conditions longitudinal abrasive wear scars between 60 m and 100 m were produced and identified. These values correspond to the applied stroke (x) of the contact wires, peak to peak value, equal to twice the oscillatory amplitude. These values depend on the running conditions and more importantly on the sheaves used, because the smaller the diameter of the sheave the more is the bending of the rope and the longer is the corresponding wear scar on the single filaments. For simulating these conditions two different stroke values of 65 m and 130 m were chosen for the tests. Due to the large influence of the contact pressure on wear two different kind of tests were performed: in the first one the crossing angle between wires was varied in five stages: 30◦ , 45◦ , 60◦ , 75◦ and 90◦ at a constant normal load so that the initial contact pressure is different in each stage and in the second one the crossing angle was varied in four stages: 45◦ , 60◦ , 75◦ and 90◦ at a constant initial contact pressure so that the normal force is different for each stage. In both cases the normal load is maintained constant during the test, so that the contact pressure changes during the test. The contact situation and corresponding wear scars are illustrated in Fig. 3. In the specific wire rope used for this study the crossing angle range of the steel wires goes from 5◦ to 45◦ [9]. Nevertheless in this study, with the aim to represent a reliable tendency of the influence of crossing angle in a general case, angles less than 30◦ were not applied because of measurement limits and the corresponding lacking measurements accuracy for the wear scar evaluation. All the tests were performed with 50,000 cycles at a constant frequency () of 10 Hz. Table 1 presents the conditions of the test series 1 in which the influence of different crossing angle was tested. To estimate the contact pressure and simplify this problem during the tests, on the basis of the elliptical contact area, only the average contact pressure in the contact point before testing was considered according to the
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Fig. 3. Illustration of different crossing angles with SEM micrographs of wear scars and corresponding initial maximum contact pressures at 1 N load.
Table 1 Set of parameters for test series 1. Parameter
Symbol
Value
Normal Load (N) Crossing angle (◦ ) Average contact pressure (MPa) Maximum contact pressure (MPa) Stroke (m) Frequency (Hz) Number of cycles (103 ) Lubricant Temperature (◦ C) Atmosphere Relative humidity (%)
Fn ˛ Pav Pmax x n
1 30◦ ; 45◦ ; 60◦ ; 75◦ ; 90◦ 1827; 2114; 2300; 2422; 2500 2246; 3171; 3450; 3633; 3750 130 ± 5 10 50 None 25 ± 1 Laboratory air 50 ± 5
T RH
well-known analytical solution for the Hertzian contact pressure distribution [10]. The average contact pressure is given by Eq. (1):
Tribosystem
B − A = 1
2
Pmax =
3 3Fn Pav = 2 2ab
(1)
where Fn is the applied normal load and a and b are the semi-axes of the elliptical contact. To obtain both semi-axes the Eqs. (2) and (3) are solved using the bisection method: 2
Rrel =
(ab) ×
(a/b) E(e) − K(e) K(e) − E(e)
3/2
=
(2)
3F R 4 n e 4Ee
2
a/b
e2
1/2
K(e) − E(e)
(3)
E(e) and K(e) are complete elliptic integrals of argument e = (1 − b2 /a2 )1/2 , b < a. Re is the equivalent radius of curvature and Rrel is the ratio of the relative curvatures R and R . Both parameters are obtained according to Eqs. (4) and (5) respectively: Re =
1 (AB)−1/2 2
Rrel =
B = A
(4)
R
(5)
R
where A and B are positive constants and are obtained solving Eqs. (6) and (7): 1 (A + B) = 2
1 1 1 1 + + + R1 R2 R1 R2
(6)
1 1 − R1 R1
2
+
1 1 − R2 R2
1 1 − R2 R2
2
1/2 cos 2˛
(7)
R1 , R1 , R2 , R2 are the principal radius of curvature of upper and bottom wire and ˛ is the crossing angle between both bodies. Ee is the composite modulus of the two contacting bodies and is obtained according to Eq. (8): Ee =
b/a
E(e) − K(e)
3/2
+2
1 1 − R1 R1
1 − 12 E1
+
1 − 22 E2
(8)
where E1 , E2 are the elastic modulus and v1 , v2 are the Poisson’s ratios of upper and bottom wires, respectively. The resolution of these equations was done with a specific program developed in Matlab® . The different average contact pressures calculated for the different crossing angles with the Young modulus of 210 MPa and the Poisson coefficient of 0.3 were: 1 N (30◦ ) (Pav = 1827 MPa), 1 N (45◦ ) (Pav = 2114 MPa), 1 N (60◦ ) (Pav = 2300 MPa), 1 N (65◦ ) (Pav = 2422 MPa) and 1 N (Pav = 2500 MPa). All these pressures are smaller than the yield strength. In this case all the tests were performed with a 130 m stroke. Table 2 presents the conditions of the test series 2 of tests in which the influence of the same initial contact pressure with different crossing angles was tested. In this case two initial contact pressures were tested: while the first one with Pav = 3200 MPa is higher than the yield strength and it is tested with a stroke of 65 m, the second one with Pav = 2500 MPa is lower than the yield strength and it is tested with a stroke of 130 m. Therefore the normal load needed to obtain these initial contact pressures are calculated accordingly for the different angles. These values are in
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Table 2 Set of parameters for test series 2. Parameter
Symbol
Value
Normal Load (N)
Fn
Crossing angle (◦ ) Average contact pressure (MPa) Maximum contact pressure (MPa) Stroke (m) Frequency (Hz) Number of cycles (103 ) Lubricant Temperature (◦ C) Atmosphere Relative humidity (%)
˛ Pav Pmax x n
2(90◦ ); 2.5(75◦ ); 3(60◦ ); 3.5(45◦ ) 1(90◦ ); 1.1(75◦ ); 1.3(60◦ ); 1.6(45◦ ) 45◦ ; 60◦ ; 75◦ ; 90◦ 3200; 2500 4800; 3750 65 ± 5; 130 ± 5 10 50 None 25 ± 1 Laboratory air 50 ± 5
T RH
the case of a contact pressure of Pav = 3200 MPa: 2 N (90◦ ), 2.5 N (75◦ ), 3 N (60◦ ), 3.5 N (45◦ ), and in the case of Pav = 2500 MPa: 1 N (90◦ ), 1.1 N (75◦ ), 1.3 N (60◦ ), 1.6 N (45◦ ). Now it is important to know what the predominant wear regime is: fretting wear or reciprocating sliding wear in both types of tests. Fretting is defined as the phenomenon occurring when two contacting surfaces are subjected to reciprocating motion of small amplitude, whereas the reciprocating wear occurs at much larger amplitude. Fouvry [11] proposed that the transition between both regimes is based on the relation between oscillatory amplitude (␦d ) and the contacting radius a, e = ıd /a: while for e < 1 fretting wear is thought to occur for e ≥ 1 reciprocating sliding wear is thought to occur. In the case of crossing angle less than 90◦ , where the contact area is an ellipse, the contact radius represents the length of semi-axis. In the test series 1, taking into account this formula and the length of semi-axis according to Eqs. (2) and (3), reciprocating sliding appears in the beginning of the tests, as it is shown in Table 3, because the e relation obtained is in the range 2.9 < e < 1.1. However Cruzado et al. [6] presented that the wear scar length increases rapidly as the tests runs for a range of loads from 0.5 N to 3 N, a range of strokes from 65 m to 130 m and a range of cycles from 20,000 to 200,000 cycles, being the e relation obtained in the range 0.23 < e < 0.82, and showing that the fretting wear is the principal regime in these type of tests. Taking into account this fact, the main wear regime during these tests is fretting, being the e relation obtained for 50,000 cycles in the range 0.27 < e < 0.59 as it is shown in Table 3. In test series 2 fretting and reciprocating sliding occurs in the beginning of the tests as it is shown in Table 4, because the e relation obtained is in the range 0.5 < e < 2.9. Nevertheless as it has been explained for test series 1 fretting is the main wear regime as the test runs. For these tests the e relation obtained for 50,000 cycles is 0.15 < e < 0.59. 2.3. Tribological quantities 2.3.1. Friction The friction behaviour is described by the coefficient of friction. The friction force as a function of the displacement is measured 120 times during a closed motion cycle. The hysteresis shows a trapezoidal shape with an inclination in the flanks due to the stiffness of the system including the fixation of the wires and the tribological contact (Fig. 4). The coefficient of friction f in each cycle is obtained by dividing the friction force Ff by the normal load Fn according to Eq. (9) and thus stored 500 times per test. However the mean coefficient of friction used in this research fav represents the average value calculated from the data of the last half of the experiment. The area enclosed by the lines of the hysteresis in Fig. 4 represents the dissipated energy for each cycle (Ed ). In order to simplify
Tribosystem
Fig. 4. Hysteresis loop of friction force Ff during one cycle of displacement equal to 2x.
the problem the accumulated dissipated energy could be estimated through the product of the average friction force (Ff,av ) and the total sliding distance (s), Eqs. (10)–(12). Taking into account the limited rigidity of the test rig the total sliding distance was obtained multiplying two times the real stroke (xreal ), which is determined on the Ff zero line (Fig. 4) and the number of cycles as it is shown in Eq. (4). The real stroke is believed to be a realistic quantity that is connected with the amount of wear, so for the calculation of friction force and the coefficient of wear this value is used [12]. Ff =
Ed 2xreal Ed =
n
(9)
Edi = Ff,av · s
(10)
i=1
Ff,av = fav · Fn
(11)
s = 2xreal · n
(12)
Ff = friction force; Ff,av = average friction force; fav = average friction coefficient; Fn = normal force; s = sliding distance; xreal = stroke; n = number of cycles; Ed = dissipated energy during one fretting cycle; Ed = accumulated dissipated friction energy for all cycles n. 2.3.2. Wear According to the contact geometry of crossed cylinders the two wires may be considered as cylindrical specimens. The planimetric wear Wq as determined by a profilometric measurement across the
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Table 3 Wear scars semi contact length limit cases for both test series 1. ˛ (◦ )
Fn (N)
◦
90 30◦ 90◦ 30◦
1 1 1 1
ıd (m)
Number of cycles (103 )
Semi contact length (m)
e
65 65 65 65
0 0 50 50
22.7 61.9 109 238
2.9 1.1 0.59 0.27
ıd (m)
Number of cycles (103 )
Semi contact length (m)
e
32.5 32.5 32.5 32.5 65 65 65 65
0 0 50 50 0 0 50 50
28.6 66.4 100 210 22.7 16.03 109.5 169.5
1.1 0.5 0.33 0.15 2.9 1.3 0.59 0.38
Table 4 Wear scars semi contact length limit cases for both test series 2. ˛ (◦ )
Fn (N)
◦
2 2 2 2 2 2 2 2
90 45◦ 90◦ 45◦ 90◦ 45◦ 90◦ 45◦
wear scar after the test is crucial for the wear volume determination and leads to the wear volume Wv as outlined in detail by Wäsche and Hartelt [7] as well as by Klaffke [13]. The detailed formulation to obtain the volumetric wear of both specimens Wv in the case of 90◦ crossed cylinders was presented by Cruzado et al. [6]. In the case of angles different from 90◦ a specific formulation for the calculation of the volumetric wear is not developed and therefore the method as described by Urchegui et al. [14] was used. Eq. (13) defines the wear coefficient k. The total volumetric wear is the sum of the wear volumes at both specimens. Eq. (14) describes the energy specific wear resistance in J/mm3 as described by Urchegui [5]. This equation considers the total dissipated frictional energy by summation over the number of cycles and relates it to the occurred wear volume and hence tells how much energy is needed to remove a certain volume due to the wear process. It therefore combines the occurring friction with the coefficient of wear. k=
WV WV = sFn 2xreal · nFn Ed
Wv
=
2xreal · nfav · Fn fav = Wv k
(13)
(14)
3. Results and discussions 3.1. Test series 1 with constant normal load 3.1.1. Friction behaviour Fig. 5 shows the friction coefficient (f) for test series 1. All these tests were done with a constant normal force of 1 N. It can be seen that the friction coefficient is almost constant but nevertheless slightly decreasing from about 0.76 to about 0.67 with increasing crossing angle, thus at higher crossing angles less frictional energy is dissipated. It is in accordance with the general tendency explained by Fouvry for metallic contacts in which an increase of the contact pressure tends to decrease the friction coefficient [15]. 3.1.2. Wear behaviour In order to analyze the wear behaviour two studies were carried out: the first one corresponds to a qualitative study of the wear, in which the wear scar was analyzed in the scanning electron microscope (SEM), and the second one corresponds to a quantitative study of the wear volume after cleaning the wear debris produced during the tests.
Fig. 5. Coefficient of friction for different crossing angles at same normal load, see Table 1.
The main wear mechanism presented in this type of tests is the tribo-oxidation as is shown in Fig. 6. While the wear particles are piled up outside wear scars (Fig. 6a), in Fig. 6b it is possible to see surface oxide which is prone to produce abrasive wear and it tends to create wear tracks in the scar during the plowing process. Analyzing the oxide wear debris (Fig. 7) two distinctive behaviours could be presented during the wear process: on one hand they may get locked between the sliding surfaces promoting three body wear, which should enhance wear volume loss, and on the other hand they may get compacted between the surfaces forming protective layers as it is seen in (Fig. 7a and b) and inducing mild wear. The last case is reported by Kato and Komai as tribo-sintering of nanometer-sized oxide [16]. Fig. 7c shows the oxide wear debris ejected outside the wear scars during the wear process. The predominant shape of theses particles is rounded as it is possible to see in Fig. 7d. The evolution of both wear scars from 30◦ to 90◦ for 1 N–130 m and 50,000 cycles are shown in Figs. 8 and 9. The tendency is clear, as the crossing angle is increased; the wear scars become more elliptical. Moreover in each wear scar is possible to see the wear tracks produced due to de plowing process mentioned previously. Fig. 10a shows the total wear volume (Wv ) for different contact angles and 1 N load. The produced wear volume is increasing
A. Cruzado et al. / Wear 273 (2011) 60–69
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Fig. 6. Wear scar surface after the test: (a) wire specimen with wear scar and debris; (b) surface inside wear scar.
with increasing contact angle. Moreover in Fig. 10b it is shown that the total linear wear increase increasing the contact angle. As a consequence of this, less cross section is obtained in the wire, being detrimental for the fatigue life of the wire rope. Fig. 10c shows the energy specific wear resistance calculated according to Eq. (6) for test series 1 with same normal loads applied for all crossing angles. It may be seen that under these conditions the energy necessary to remove 1 mm3 is slightly decreasing from 22 × 103 J to 16 × 103 J with increasing crossing angle from
30◦ to 90◦ which means that at higher crossing angles less energy is needed to achieve the same amount of wear, or in other words, the wear process is more intense. With a constant or decreasing friction coefficient, as it was observed, at the same time this means that the coefficient of wear (k) is increasing. This can be seen in Fig. 10d. Since the load is constant (and so is the cycle number) in this test series, an increasing coefficient of wear could be explained by 2 different reasons. First, the wear mechanism is different for all crossing angles. Or second, there is a different ratio of running in to steady state process. This
Fig. 7. Oxide wear particles: (a) inside wear scar; (b) compacted wear particles; (c) outside wear scar and (d) shape of oxide wear particle.
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Fig. 8. Wear scars in upper wire (cylinder 1: static): (a) Fn = 1 N, x = 130 m, ˛ = 30◦ ; (b) Fn = 1 N, x = 130 m, ˛ = 60◦ ; (c) Fn = 1 N, x = 130 m, ˛ = 90◦ .
Fig. 9. Wear scars in bottom wire (cylinder 2: moving): (a) Fn = 1 N, x = 130 m, ˛ = 30◦ ; (b) Fn = 1 N, x = 130 m, ˛ = 60◦ ; (c) Fn = 1 N, x = 130 m, ˛ = 90◦ .
Fig. 10. Wear results for different contact angles and 1 N load: (a) Total linear wear; (b) Total volumetric wear; (c) Energy specific wear resistance; (d) Coefficient of wear for test series 1.
A. Cruzado et al. / Wear 273 (2011) 60–69
Fig. 11. Running-in period and steady state period in tests with 90◦ crossing angle [6].
last possibility is analyzed in Fig. 11. This figure shows the total volumetric wear versus Archard’s loading factor, as defined in [17], for tests carried out with 90◦ crossing angle and different normal loads. It can observe that for each normal load there is a distinctive difference between an initial running in period with higher slope and a steady state period with a significantly lower slope. The running in period is represented by the first slope, which points at a higher wear intensity and is longer for higher contact pressures. The steady state period is represented by the second slope and it seems to increase with increasing contact pressures. Taking into account the wear mechanism described before, it looks that: on one hand the formation of protective layers could be the reason of the transition from a severe wear process to a mild wear process and on the other hand the formation of these layers is earlier with smaller contact pressures. For this reason, the smaller crossing angle, in which less contact pressure is obtained, tends to produce smaller coefficients of wear and also higher energy specific wear resistance. Based on the previous assumptions the second reason is much more probable and therefore the test results point at a crucial dependence of the running in process from the contact situation. However, this was not further deepened in this study.
3.2. Test series 2 with same contact pressure 3.2.1. Friction behaviour Fig. 12 shows the coefficient of friction for tests where the average contact pressure is kept constant and for two different strokes. In this case the friction coefficient (f) does not change significantly.
67
Fig. 12. Coefficient of friction for different crossing angles and same initial average contact pressure.
3.2.2. Wear behaviour The wear scars after the test series 2 from 45◦ to 90◦ for 3200 Mpa–130 m and 50,000 cycles are shown in Figs. 13 and 14. Considering the wear mechanism described in Section 3.1.2, in both wear scars is possible to see the wear tracks. Fig. 15a shows the total wear volume (Wv ) for different crossing angles and 2 different strokes and contact pressures. In contrast to the results of test series 1 the wear volume tends to decrease with increasing crossing angle: less wear at higher angle. Furthermore the linear wear tends to decrease slightly with increasing crossing angle as it shows Fig. 15b. Fig. 15c shows the energy specific wear resistance for this test series 2. It can be noticed that the wear resistance is more or less constant and does not change significantly taking into account the experimental error. The energy needed to remove 1 mm3 is about 18 × 103 J. Under these test conditions the wear intensity is roughly not dependent on the crossing angle besides the very slight tendency towards a slight minimum at an angle of 60◦ which is not interpreted further. With this result according to Eq. (6) hence the coefficient of wear (k) must be also more or less constant since the coefficient of friction is constant. This can be seen in Fig. 15d. The energetic consideration leads then to the conclusion that under condition of test series 2, with the same average contact pressure, the wear intensity is roughly constant and, therefore, independent from the crossing angle. In accordance with the conditions that the contact pressure is largely kept constant by adjusting the normal load for the different crossing angles the wear intensity should also be largely constant. In accordance with the results from test series 1 in this case the coefficient of wear could be constant, as seen in Fig. 15d, because the ratio between the running in
Fig. 13. Wear scars in upper wire (cylinder 1: static): (a) Fn = 1.6 N, x = 130 m, ˛ = 45◦ ; (b) Fn = 1.1 N, x = 130 m, ˛ = 75◦ ; (c) Fn = 1 N, x = 130 m, ˛ = 90◦ .
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Fig. 14. Wear scars in bottom wire (cylinder 2: moving): (a) Fn = 1.6 N, x = 130 m, ˛ = 45◦ ; (b) Fn = 1.1 N, x = 130 m, ˛ = 75◦ ; (c) Fn = 1 N, x = 130 m, ˛ = 90◦ .
process and the following steady state process is kept constant which most probably is a consequence of the constant contact pressure. The observed decrease of the wear volume as shown in Fig. 15a is explained as a consequence of the decreasing normal load in this test series. The final remark comes from the similar values obtained from volumetric wear (Wv ), in Fig. 15a, and also from the coefficient of wear (k), in Fig. 15d, between the two contact pressure tests: 3200 MPa with a stroke of 65 m and 2500 MPa with a stroke of 130 m. Cruzado et al. [6] reported that in the case of 90◦ crossing angle tests, the same magnitude of Fn × s (the Archard’s loading factor) produces the same running in period and the same steady state
period, in other words, the same wear mechanism, in two specific cases: 0.5 N 130 m/1 N 65 m and in 1 N 130 m/2 N 65 m. This last case is shown in Fig. 15 for 90◦ crossing angle. Taking into account that the contact pressure is directly related with the normal force Fn and the contact angle ˛, it could be related the stroke and the contact pressure with the wear behaviour. Considering the contact pressures used in these tests, it could be defined a relation Pav × s which could explain the same wear mechanism for these specific tests. This relation is presented in Eq. (15): Psm × sgt 1.59 Pgt × ssm
(15)
Fig. 15. Wear results for different contact angles and 2 different initial average contact pressures and strokes: (a) total linear wear; (b) total volumetric wear; (c) energy specific wear resistance; (d) coefficient of wear for test series 1.
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with Pgt = greater contact pressure (3200 Mpa); ssm = smaller stroke (65 m); Psm = smaller contact pressure (2500 Mpa) and sgt = greater stroke (130 m). After this it is important to know that the wear behaviour of both periods (running in period and steady state period) not only depends on the contact pressure but it depends on the relation of contact pressure–stroke.
under the Universidad Empresa programme in the frame of the SIVICA project (Ref. UE2009-5) as well as from European Commission in the frame of the ERASMUS programme and from BAM Federal Institute for Materials Research and Testing is gratefully acknowledged.
4. Summary and conclusions
[1] R.B. Waterhouse, Fretting Fatigue, Applied Science Publishers Ltd., London, 1981. [2] K.K. Schrems, Wear related fatigue in a wire rope failure, Journal of Testing & Evaluation 22 (1994) 490–499. [3] R.B. Waterhouse, Fretting in steel ropes and cable—a review, ASTM Special Technical Publication 1425 (2002) 3–14. [4] R.B. Waterhouse, D.E. Taylor, Fretting fatigue in steel ropes, Lubrication Engineering 27 (1971) 123–127. [5] M.A. Urchegui, M. Hartelt, D. Klaffke, X. Gómez, Laboratory fretting tests with thin wire specimens, Tribotest 13 (2007) 67–81. [6] A. Cruzado, M. Hartelt, R. Wäsche, M.A. Urchegui, X. Gómez, Fretting wear of thin steel wires. Part 1: influence of contact pressure, Wear 268 (2010) 1409–1416. [7] R. Wäsche, M. Hartelt, Wear testing with crossed cylinders—comparison of methods, in: W.J. Bartz (Ed.), Proceedings 16th International Colloquium on Tribology, Technische Akademie Esslingen, Ostfildern, January 15–17, 2008. [8] D. Klaffke, On the influence of test parameters on friction and wear of ceramics in oscillating sliding contacts, TriboTest 1 (1995) 311–320. [9] M.A. Urchegui, W. Tato, X. Gómez, Wear evolution in a stranded rope subjected to cyclic bending, Journal of Materials Engineering and Performance 17 (2007) 550–560. [10] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985. [11] S. Fouvry, Etude quantitative des dégradations en fretting [Quantitative aspects of fretting damages], PhD Thesis, 97–04, Ecole Central de Lyon, Ecully, France, 1997. [12] D. Klaffke, Towards a tribological reference test-fretting test? TriboTest 12 (2006) 11. [13] D. Klaffke, Fretting wear of ceramics, Tribology International 22 (1989) 89–101. [14] M.A. Urchegui, X. Gómez, W. Tato, A method for evaluating fretting wear scars in thin steel roping wires based on confocal imaging profilometry, Journal of Testing and Evaluation 35 (2007) 357–363. [15] S. Fouvry, Shakedown analysis and fretting wear response under gross slip condition, Wear 251 (2001) 1320–1331. [16] H. Kato, k. Komai, Tribofilm formation and mild wear by tribo-sintering of nanometer-sized oxide particles on rubbing steel surfaces, Wear 262 (2007) 36–41. [17] S. Fouvry, T. Liskiewicz, C. Paulin, A global-local wear approach to quantify the contact endurance under reciprocating-fretting sliding conditions, Wear 263 (2007) 518–531.
Oscillating sliding tests were carried out on thin steel wires under fretting conditions using the crossed cylinders contact geometry. The main parameters were the crossing angle and the contact pressure. The crossing angle was varied between 30◦ and 90◦ . Two different types of test were carried out. In the first test series the normal load was kept constant at 1 N which leads to different initial contact pressures according to the applied crossing angle. In the second test series the normal load was adjusted in that way that the initial contact pressure is largely kept constant at all crossing angles. The results show that the generated wear volume is mainly dependent on the normal load. The consideration of the accumulated dissipated energy leads to an energy specific wear resistance as a measure of the wear intensity. The results may be understood assuming two different wear periods namely a running-in period and a steady state period with two different wear coefficients. The transition of these two periods could be attributed to the formation of oxide protective layers. A varying length of the running-in period due to a changing contact pressure would then result in a different wear coefficient, as seen in test series 1. A constant ratio between the running in process and the following steady state process due to a constant contact pressure would then explain the constant wear coefficients in test series 2. Finally it is important to remark that the wear behaviour of both periods depends on the relation contact pressure–stroke. Acknowledgements The authors would like to thank Christine Neumann for technical assistance. The financial support from Basque Government
References
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Wear journal homepage: www.elsevier.com/locate/wear
Fretting wear of thin steel wires. Part 2: Influence of crossing angle A. Cruzado a,∗ , M. Hartelt b , R. Wäsche b , M.A. Urchegui c , X. Gómez a a
Mondragon Goi Eskola Politeknikoa, Mondragon Unibertsitatea, Loramendi 4, 20500 Arrasate-Mondragon, Spain BAM Federal Institute for Materials Research and Testing, Unter den Eichen 44–46, D-12203 Berlin, Germany c ORONA eic, Polígono Industrial Lastaola s/n, 20120 Hernani, Spain b
a r t i c l e
i n f o
Article history: Received 2 September 2010 Received in revised form 11 April 2011 Accepted 21 April 2011 Available online 17 June 2011 Keywords: Fretting Wires Contact pressure Crossing angle
a b s t r a c t The wear behaviour of thin steel wires has been analyzed under oscillating sliding conditions in crossed cylinders contact geometry. The focus of this analysis was the influence of the crossing angle between the wires on the wear. The wires used had 0.45 mm in diameter and the material was cold-drawn eutectoid carbon steel (0.8% C) with a tensile strength higher than 2800 MPa. Two different types of tests were carried out, the first one representing the influence of the crossing angle for a constant load and the second one representing the influence of the crossing angle with constant contact pressure. In the first type of tests it was seen that as the contact angle decreases the contact pressure decreases too and hence less energy specific wear resistance is observed. As a consequence less wear is produced, thus increasing the life of the wires. In the second type of tests it was seen that with constant contact pressure but different crossing angles, nearly the same energy specific wear resistance was observed. This points at an identical wear behaviour in both type of tests but with a running-in and a steady state period as two different wear periods. The tests showed that the running in period may play an important role in the overall wear particle generation and hence the wear occurring in the steady state period is rather mild. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Steel wires in form of thin wires are used to construct wire ropes being used in many industrial applications, like structural elements (reinforcement for tires, bridges, barges etc.) or as elements for transporting purposes (cranes, lifts, funicular railway, ski lifts) due to their high axial strength and bending flexibility. These mechanical properties of the ropes are largely dependent on their construction and the properties of the wires itself, because the wires are wound into strands, which are then wound to form the rope (Fig. 1). The properties of the rope depend on the number, size and arrangement of the wires in the strands, the number and arrangement of the strands and the core type. Despite their outstanding mechanical properties steel wire ropes are prone to degradation due to fretting damage [1]. If tensile loads are applied and/or released, or the rope runs over a sheave, the contact pressures between wires change and oscillatory motions between the contacting wires occur. Due to the bending when the ropes run over the sheaves, the stress in the contact area is largely increasing. Under the oscillatory motion between the wires this leads to increased wear [2,3] and subsequently producing the failure of the rope. The effect of fretting wear is especially important in point con-
∗ Corresponding author. Tel.: +34 943 73 96 92; fax: +34 943 79 15 36. E-mail address: [email protected] (A. Cruzado). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.04.012
tacts (typically between the outermost wires of strands and core or between the outermost wires of adjacent strands). Since the wear is directly dependent on the bending of the rope, until now the radius of the sheave had to be large so that security tolerance was large enough to avoid catastrophic failure of the rope during the operating time period. Under compulsion of smaller space for elevating units lift manufacturers want to use smaller sheaves with the aim of reducing the dimensions of the electric motor. Smaller sheave diameters lead to higher bending of the rope and consequently to a higher wear of the wires and a considerable decrease of the fatigue lifetime of the ropes [4]. For further understanding of rope degradation mechanisms it is important to analyze the wear mechanisms occurring in the different parts of the rope during service. Since fretting wear reduces the diameter of the wires, it is one of the main reasons for a shortened life time of a wire and therefore adds an important contribution to the degradation of the rope of this type of wires in fretting conditions dependant on different parameters like sliding length, frequency and contact pressure. Urchegui [5] analyzed fretting wear of thin steel wires using different operational variables like normal force, stroke and number of cycles. This investigation was continued with a widened parameter field [6] mainly with an extension to the parameters normal load and loading time (number of cycles). In both cases, the crossing angle was 90◦ . The main conclusion was that the wires are submitted to two distinctive behaviours: one corresponds to the
A. Cruzado et al. / Wear 273 (2011) 60–69
Fig. 1. Schematic of a wire rope composed of different strands of wound steel filaments.
running-in period, with a more aggressive wear behaviour, and the second one corresponds to the stable period with mild wear behaviour. However, both are in close relation with the contact pressure. In this paper with the aim of representing a more realistic wire contact configuration, different tests with different crossing angles were performed. Taking into account the influence of the contact pressure in the wear behaviour two types of tests were performed: the first one corresponds to maintaining the same load for different crossing angles, so that the mean contact pressure changes during the test due to wear and the second type of test is aimed at maintaining the same mean contact pressure for different crossing angles. However, the mean contact pressure can only be known in the beginning of the test, not during the ongoing test with time. This influence therefore has not been studied. 2. Experimental details 2.1. Tribological testing For tribological testing the contact geometry of crossed cylinders was used to simulate the fretting wear behaviour of the wires in ropes. This method allows for an exact determination of wear under the required conditions [5,7]. The wires used for the experiments are wires which are usually fabricated into a 7 × 19 rope (7 strands with 19 individual wires in each one). The diameters of the wires are different and range from 0.22 mm to 0.45 mm (Fig. 1). For the tests, wires with a diameter of 0.45 mm, were used. They are cold-drawn from eutectoid carbon steel with 0.8% C with a tensile strength greater than 2800 MPa and a hardness of 659 ± 81 HV 0.05. The surface average roughness (Ra ) of these wires along its axis was 0.35 and 0.70 m in perpendicular direction. These values were obtained from the measurements carried out at an unworn wire using a confocal imaging profiler (Pl, Sensofar). The wires are usually covered with a thin film of brass with a film thickness of less than 1 m (Fig. 2), of which the exact composition is unknown. The chemical composition of the film brass was qualitatively analyzed by energy dispersive X-ray microanalysis (EDS) in the scanning electron microscope (SEM), in which peaks of Cu and Zn, typical chemical elements of the brass, were observed. Fretting wear tests were carried out on a tribometer which is described in more detail in [6,8]. During each test the real stroke (xreal ), friction force (Ff ) and total linear wear (Wl,tot ) were measured. Relative humidity (RH) and temperature (T) were kept constant during the test. All measured quantities were recorded
61
Fig. 2. SEM micrograph of Brass film cover in a longitudinal cut of the wire.
on-line multiple times. After each test friction and wear quantities are derived from the stored values. The planimetric wear (Wq ) and the volumetric wear (Wv ) subsequently determined from wear scar profilometry (Hommeltester, Fa. Hommel, Homburg, Germany) as described in detail by Wäsche and Hartelt [7]. 2.2. Test program Based on an analysis in an earlier study it was known that in a new unused rope plastic deformation appeared. Therefore in these tests the value of average contact pressure was chosen to be higher or lower than the yield strength of the wires (2800 MPa). Furthermore the selection of the oscillating amplitude was done based on a simulation study. In this study a real situation was simulated with a rope running over a sheave of 200 mm diameter. Under these conditions longitudinal abrasive wear scars between 60 m and 100 m were produced and identified. These values correspond to the applied stroke (x) of the contact wires, peak to peak value, equal to twice the oscillatory amplitude. These values depend on the running conditions and more importantly on the sheaves used, because the smaller the diameter of the sheave the more is the bending of the rope and the longer is the corresponding wear scar on the single filaments. For simulating these conditions two different stroke values of 65 m and 130 m were chosen for the tests. Due to the large influence of the contact pressure on wear two different kind of tests were performed: in the first one the crossing angle between wires was varied in five stages: 30◦ , 45◦ , 60◦ , 75◦ and 90◦ at a constant normal load so that the initial contact pressure is different in each stage and in the second one the crossing angle was varied in four stages: 45◦ , 60◦ , 75◦ and 90◦ at a constant initial contact pressure so that the normal force is different for each stage. In both cases the normal load is maintained constant during the test, so that the contact pressure changes during the test. The contact situation and corresponding wear scars are illustrated in Fig. 3. In the specific wire rope used for this study the crossing angle range of the steel wires goes from 5◦ to 45◦ [9]. Nevertheless in this study, with the aim to represent a reliable tendency of the influence of crossing angle in a general case, angles less than 30◦ were not applied because of measurement limits and the corresponding lacking measurements accuracy for the wear scar evaluation. All the tests were performed with 50,000 cycles at a constant frequency () of 10 Hz. Table 1 presents the conditions of the test series 1 in which the influence of different crossing angle was tested. To estimate the contact pressure and simplify this problem during the tests, on the basis of the elliptical contact area, only the average contact pressure in the contact point before testing was considered according to the
62
A. Cruzado et al. / Wear 273 (2011) 60–69
Fig. 3. Illustration of different crossing angles with SEM micrographs of wear scars and corresponding initial maximum contact pressures at 1 N load.
Table 1 Set of parameters for test series 1. Parameter
Symbol
Value
Normal Load (N) Crossing angle (◦ ) Average contact pressure (MPa) Maximum contact pressure (MPa) Stroke (m) Frequency (Hz) Number of cycles (103 ) Lubricant Temperature (◦ C) Atmosphere Relative humidity (%)
Fn ˛ Pav Pmax x n
1 30◦ ; 45◦ ; 60◦ ; 75◦ ; 90◦ 1827; 2114; 2300; 2422; 2500 2246; 3171; 3450; 3633; 3750 130 ± 5 10 50 None 25 ± 1 Laboratory air 50 ± 5
T RH
well-known analytical solution for the Hertzian contact pressure distribution [10]. The average contact pressure is given by Eq. (1):
Tribosystem
B − A = 1
2
Pmax =
3 3Fn Pav = 2 2ab
(1)
where Fn is the applied normal load and a and b are the semi-axes of the elliptical contact. To obtain both semi-axes the Eqs. (2) and (3) are solved using the bisection method: 2
Rrel =
(ab) ×
(a/b) E(e) − K(e) K(e) − E(e)
3/2
=
(2)
3F R 4 n e 4Ee
2
a/b
e2
1/2
K(e) − E(e)
(3)
E(e) and K(e) are complete elliptic integrals of argument e = (1 − b2 /a2 )1/2 , b < a. Re is the equivalent radius of curvature and Rrel is the ratio of the relative curvatures R and R . Both parameters are obtained according to Eqs. (4) and (5) respectively: Re =
1 (AB)−1/2 2
Rrel =
B = A
(4)
R
(5)
R
where A and B are positive constants and are obtained solving Eqs. (6) and (7): 1 (A + B) = 2
1 1 1 1 + + + R1 R2 R1 R2
(6)
1 1 − R1 R1
2
+
1 1 − R2 R2
1 1 − R2 R2
2
1/2 cos 2˛
(7)
R1 , R1 , R2 , R2 are the principal radius of curvature of upper and bottom wire and ˛ is the crossing angle between both bodies. Ee is the composite modulus of the two contacting bodies and is obtained according to Eq. (8): Ee =
b/a
E(e) − K(e)
3/2
+2
1 1 − R1 R1
1 − 12 E1
+
1 − 22 E2
(8)
where E1 , E2 are the elastic modulus and v1 , v2 are the Poisson’s ratios of upper and bottom wires, respectively. The resolution of these equations was done with a specific program developed in Matlab® . The different average contact pressures calculated for the different crossing angles with the Young modulus of 210 MPa and the Poisson coefficient of 0.3 were: 1 N (30◦ ) (Pav = 1827 MPa), 1 N (45◦ ) (Pav = 2114 MPa), 1 N (60◦ ) (Pav = 2300 MPa), 1 N (65◦ ) (Pav = 2422 MPa) and 1 N (Pav = 2500 MPa). All these pressures are smaller than the yield strength. In this case all the tests were performed with a 130 m stroke. Table 2 presents the conditions of the test series 2 of tests in which the influence of the same initial contact pressure with different crossing angles was tested. In this case two initial contact pressures were tested: while the first one with Pav = 3200 MPa is higher than the yield strength and it is tested with a stroke of 65 m, the second one with Pav = 2500 MPa is lower than the yield strength and it is tested with a stroke of 130 m. Therefore the normal load needed to obtain these initial contact pressures are calculated accordingly for the different angles. These values are in
A. Cruzado et al. / Wear 273 (2011) 60–69
63
Table 2 Set of parameters for test series 2. Parameter
Symbol
Value
Normal Load (N)
Fn
Crossing angle (◦ ) Average contact pressure (MPa) Maximum contact pressure (MPa) Stroke (m) Frequency (Hz) Number of cycles (103 ) Lubricant Temperature (◦ C) Atmosphere Relative humidity (%)
˛ Pav Pmax x n
2(90◦ ); 2.5(75◦ ); 3(60◦ ); 3.5(45◦ ) 1(90◦ ); 1.1(75◦ ); 1.3(60◦ ); 1.6(45◦ ) 45◦ ; 60◦ ; 75◦ ; 90◦ 3200; 2500 4800; 3750 65 ± 5; 130 ± 5 10 50 None 25 ± 1 Laboratory air 50 ± 5
T RH
the case of a contact pressure of Pav = 3200 MPa: 2 N (90◦ ), 2.5 N (75◦ ), 3 N (60◦ ), 3.5 N (45◦ ), and in the case of Pav = 2500 MPa: 1 N (90◦ ), 1.1 N (75◦ ), 1.3 N (60◦ ), 1.6 N (45◦ ). Now it is important to know what the predominant wear regime is: fretting wear or reciprocating sliding wear in both types of tests. Fretting is defined as the phenomenon occurring when two contacting surfaces are subjected to reciprocating motion of small amplitude, whereas the reciprocating wear occurs at much larger amplitude. Fouvry [11] proposed that the transition between both regimes is based on the relation between oscillatory amplitude (␦d ) and the contacting radius a, e = ıd /a: while for e < 1 fretting wear is thought to occur for e ≥ 1 reciprocating sliding wear is thought to occur. In the case of crossing angle less than 90◦ , where the contact area is an ellipse, the contact radius represents the length of semi-axis. In the test series 1, taking into account this formula and the length of semi-axis according to Eqs. (2) and (3), reciprocating sliding appears in the beginning of the tests, as it is shown in Table 3, because the e relation obtained is in the range 2.9 < e < 1.1. However Cruzado et al. [6] presented that the wear scar length increases rapidly as the tests runs for a range of loads from 0.5 N to 3 N, a range of strokes from 65 m to 130 m and a range of cycles from 20,000 to 200,000 cycles, being the e relation obtained in the range 0.23 < e < 0.82, and showing that the fretting wear is the principal regime in these type of tests. Taking into account this fact, the main wear regime during these tests is fretting, being the e relation obtained for 50,000 cycles in the range 0.27 < e < 0.59 as it is shown in Table 3. In test series 2 fretting and reciprocating sliding occurs in the beginning of the tests as it is shown in Table 4, because the e relation obtained is in the range 0.5 < e < 2.9. Nevertheless as it has been explained for test series 1 fretting is the main wear regime as the test runs. For these tests the e relation obtained for 50,000 cycles is 0.15 < e < 0.59. 2.3. Tribological quantities 2.3.1. Friction The friction behaviour is described by the coefficient of friction. The friction force as a function of the displacement is measured 120 times during a closed motion cycle. The hysteresis shows a trapezoidal shape with an inclination in the flanks due to the stiffness of the system including the fixation of the wires and the tribological contact (Fig. 4). The coefficient of friction f in each cycle is obtained by dividing the friction force Ff by the normal load Fn according to Eq. (9) and thus stored 500 times per test. However the mean coefficient of friction used in this research fav represents the average value calculated from the data of the last half of the experiment. The area enclosed by the lines of the hysteresis in Fig. 4 represents the dissipated energy for each cycle (Ed ). In order to simplify
Tribosystem
Fig. 4. Hysteresis loop of friction force Ff during one cycle of displacement equal to 2x.
the problem the accumulated dissipated energy could be estimated through the product of the average friction force (Ff,av ) and the total sliding distance (s), Eqs. (10)–(12). Taking into account the limited rigidity of the test rig the total sliding distance was obtained multiplying two times the real stroke (xreal ), which is determined on the Ff zero line (Fig. 4) and the number of cycles as it is shown in Eq. (4). The real stroke is believed to be a realistic quantity that is connected with the amount of wear, so for the calculation of friction force and the coefficient of wear this value is used [12]. Ff =
Ed 2xreal Ed =
n
(9)
Edi = Ff,av · s
(10)
i=1
Ff,av = fav · Fn
(11)
s = 2xreal · n
(12)
Ff = friction force; Ff,av = average friction force; fav = average friction coefficient; Fn = normal force; s = sliding distance; xreal = stroke; n = number of cycles; Ed = dissipated energy during one fretting cycle; Ed = accumulated dissipated friction energy for all cycles n. 2.3.2. Wear According to the contact geometry of crossed cylinders the two wires may be considered as cylindrical specimens. The planimetric wear Wq as determined by a profilometric measurement across the
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A. Cruzado et al. / Wear 273 (2011) 60–69
Table 3 Wear scars semi contact length limit cases for both test series 1. ˛ (◦ )
Fn (N)
◦
90 30◦ 90◦ 30◦
1 1 1 1
ıd (m)
Number of cycles (103 )
Semi contact length (m)
e
65 65 65 65
0 0 50 50
22.7 61.9 109 238
2.9 1.1 0.59 0.27
ıd (m)
Number of cycles (103 )
Semi contact length (m)
e
32.5 32.5 32.5 32.5 65 65 65 65
0 0 50 50 0 0 50 50
28.6 66.4 100 210 22.7 16.03 109.5 169.5
1.1 0.5 0.33 0.15 2.9 1.3 0.59 0.38
Table 4 Wear scars semi contact length limit cases for both test series 2. ˛ (◦ )
Fn (N)
◦
2 2 2 2 2 2 2 2
90 45◦ 90◦ 45◦ 90◦ 45◦ 90◦ 45◦
wear scar after the test is crucial for the wear volume determination and leads to the wear volume Wv as outlined in detail by Wäsche and Hartelt [7] as well as by Klaffke [13]. The detailed formulation to obtain the volumetric wear of both specimens Wv in the case of 90◦ crossed cylinders was presented by Cruzado et al. [6]. In the case of angles different from 90◦ a specific formulation for the calculation of the volumetric wear is not developed and therefore the method as described by Urchegui et al. [14] was used. Eq. (13) defines the wear coefficient k. The total volumetric wear is the sum of the wear volumes at both specimens. Eq. (14) describes the energy specific wear resistance in J/mm3 as described by Urchegui [5]. This equation considers the total dissipated frictional energy by summation over the number of cycles and relates it to the occurred wear volume and hence tells how much energy is needed to remove a certain volume due to the wear process. It therefore combines the occurring friction with the coefficient of wear. k=
WV WV = sFn 2xreal · nFn Ed
Wv
=
2xreal · nfav · Fn fav = Wv k
(13)
(14)
3. Results and discussions 3.1. Test series 1 with constant normal load 3.1.1. Friction behaviour Fig. 5 shows the friction coefficient (f) for test series 1. All these tests were done with a constant normal force of 1 N. It can be seen that the friction coefficient is almost constant but nevertheless slightly decreasing from about 0.76 to about 0.67 with increasing crossing angle, thus at higher crossing angles less frictional energy is dissipated. It is in accordance with the general tendency explained by Fouvry for metallic contacts in which an increase of the contact pressure tends to decrease the friction coefficient [15]. 3.1.2. Wear behaviour In order to analyze the wear behaviour two studies were carried out: the first one corresponds to a qualitative study of the wear, in which the wear scar was analyzed in the scanning electron microscope (SEM), and the second one corresponds to a quantitative study of the wear volume after cleaning the wear debris produced during the tests.
Fig. 5. Coefficient of friction for different crossing angles at same normal load, see Table 1.
The main wear mechanism presented in this type of tests is the tribo-oxidation as is shown in Fig. 6. While the wear particles are piled up outside wear scars (Fig. 6a), in Fig. 6b it is possible to see surface oxide which is prone to produce abrasive wear and it tends to create wear tracks in the scar during the plowing process. Analyzing the oxide wear debris (Fig. 7) two distinctive behaviours could be presented during the wear process: on one hand they may get locked between the sliding surfaces promoting three body wear, which should enhance wear volume loss, and on the other hand they may get compacted between the surfaces forming protective layers as it is seen in (Fig. 7a and b) and inducing mild wear. The last case is reported by Kato and Komai as tribo-sintering of nanometer-sized oxide [16]. Fig. 7c shows the oxide wear debris ejected outside the wear scars during the wear process. The predominant shape of theses particles is rounded as it is possible to see in Fig. 7d. The evolution of both wear scars from 30◦ to 90◦ for 1 N–130 m and 50,000 cycles are shown in Figs. 8 and 9. The tendency is clear, as the crossing angle is increased; the wear scars become more elliptical. Moreover in each wear scar is possible to see the wear tracks produced due to de plowing process mentioned previously. Fig. 10a shows the total wear volume (Wv ) for different contact angles and 1 N load. The produced wear volume is increasing
A. Cruzado et al. / Wear 273 (2011) 60–69
65
Fig. 6. Wear scar surface after the test: (a) wire specimen with wear scar and debris; (b) surface inside wear scar.
with increasing contact angle. Moreover in Fig. 10b it is shown that the total linear wear increase increasing the contact angle. As a consequence of this, less cross section is obtained in the wire, being detrimental for the fatigue life of the wire rope. Fig. 10c shows the energy specific wear resistance calculated according to Eq. (6) for test series 1 with same normal loads applied for all crossing angles. It may be seen that under these conditions the energy necessary to remove 1 mm3 is slightly decreasing from 22 × 103 J to 16 × 103 J with increasing crossing angle from
30◦ to 90◦ which means that at higher crossing angles less energy is needed to achieve the same amount of wear, or in other words, the wear process is more intense. With a constant or decreasing friction coefficient, as it was observed, at the same time this means that the coefficient of wear (k) is increasing. This can be seen in Fig. 10d. Since the load is constant (and so is the cycle number) in this test series, an increasing coefficient of wear could be explained by 2 different reasons. First, the wear mechanism is different for all crossing angles. Or second, there is a different ratio of running in to steady state process. This
Fig. 7. Oxide wear particles: (a) inside wear scar; (b) compacted wear particles; (c) outside wear scar and (d) shape of oxide wear particle.
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A. Cruzado et al. / Wear 273 (2011) 60–69
Fig. 8. Wear scars in upper wire (cylinder 1: static): (a) Fn = 1 N, x = 130 m, ˛ = 30◦ ; (b) Fn = 1 N, x = 130 m, ˛ = 60◦ ; (c) Fn = 1 N, x = 130 m, ˛ = 90◦ .
Fig. 9. Wear scars in bottom wire (cylinder 2: moving): (a) Fn = 1 N, x = 130 m, ˛ = 30◦ ; (b) Fn = 1 N, x = 130 m, ˛ = 60◦ ; (c) Fn = 1 N, x = 130 m, ˛ = 90◦ .
Fig. 10. Wear results for different contact angles and 1 N load: (a) Total linear wear; (b) Total volumetric wear; (c) Energy specific wear resistance; (d) Coefficient of wear for test series 1.
A. Cruzado et al. / Wear 273 (2011) 60–69
Fig. 11. Running-in period and steady state period in tests with 90◦ crossing angle [6].
last possibility is analyzed in Fig. 11. This figure shows the total volumetric wear versus Archard’s loading factor, as defined in [17], for tests carried out with 90◦ crossing angle and different normal loads. It can observe that for each normal load there is a distinctive difference between an initial running in period with higher slope and a steady state period with a significantly lower slope. The running in period is represented by the first slope, which points at a higher wear intensity and is longer for higher contact pressures. The steady state period is represented by the second slope and it seems to increase with increasing contact pressures. Taking into account the wear mechanism described before, it looks that: on one hand the formation of protective layers could be the reason of the transition from a severe wear process to a mild wear process and on the other hand the formation of these layers is earlier with smaller contact pressures. For this reason, the smaller crossing angle, in which less contact pressure is obtained, tends to produce smaller coefficients of wear and also higher energy specific wear resistance. Based on the previous assumptions the second reason is much more probable and therefore the test results point at a crucial dependence of the running in process from the contact situation. However, this was not further deepened in this study.
3.2. Test series 2 with same contact pressure 3.2.1. Friction behaviour Fig. 12 shows the coefficient of friction for tests where the average contact pressure is kept constant and for two different strokes. In this case the friction coefficient (f) does not change significantly.
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Fig. 12. Coefficient of friction for different crossing angles and same initial average contact pressure.
3.2.2. Wear behaviour The wear scars after the test series 2 from 45◦ to 90◦ for 3200 Mpa–130 m and 50,000 cycles are shown in Figs. 13 and 14. Considering the wear mechanism described in Section 3.1.2, in both wear scars is possible to see the wear tracks. Fig. 15a shows the total wear volume (Wv ) for different crossing angles and 2 different strokes and contact pressures. In contrast to the results of test series 1 the wear volume tends to decrease with increasing crossing angle: less wear at higher angle. Furthermore the linear wear tends to decrease slightly with increasing crossing angle as it shows Fig. 15b. Fig. 15c shows the energy specific wear resistance for this test series 2. It can be noticed that the wear resistance is more or less constant and does not change significantly taking into account the experimental error. The energy needed to remove 1 mm3 is about 18 × 103 J. Under these test conditions the wear intensity is roughly not dependent on the crossing angle besides the very slight tendency towards a slight minimum at an angle of 60◦ which is not interpreted further. With this result according to Eq. (6) hence the coefficient of wear (k) must be also more or less constant since the coefficient of friction is constant. This can be seen in Fig. 15d. The energetic consideration leads then to the conclusion that under condition of test series 2, with the same average contact pressure, the wear intensity is roughly constant and, therefore, independent from the crossing angle. In accordance with the conditions that the contact pressure is largely kept constant by adjusting the normal load for the different crossing angles the wear intensity should also be largely constant. In accordance with the results from test series 1 in this case the coefficient of wear could be constant, as seen in Fig. 15d, because the ratio between the running in
Fig. 13. Wear scars in upper wire (cylinder 1: static): (a) Fn = 1.6 N, x = 130 m, ˛ = 45◦ ; (b) Fn = 1.1 N, x = 130 m, ˛ = 75◦ ; (c) Fn = 1 N, x = 130 m, ˛ = 90◦ .
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Fig. 14. Wear scars in bottom wire (cylinder 2: moving): (a) Fn = 1.6 N, x = 130 m, ˛ = 45◦ ; (b) Fn = 1.1 N, x = 130 m, ˛ = 75◦ ; (c) Fn = 1 N, x = 130 m, ˛ = 90◦ .
process and the following steady state process is kept constant which most probably is a consequence of the constant contact pressure. The observed decrease of the wear volume as shown in Fig. 15a is explained as a consequence of the decreasing normal load in this test series. The final remark comes from the similar values obtained from volumetric wear (Wv ), in Fig. 15a, and also from the coefficient of wear (k), in Fig. 15d, between the two contact pressure tests: 3200 MPa with a stroke of 65 m and 2500 MPa with a stroke of 130 m. Cruzado et al. [6] reported that in the case of 90◦ crossing angle tests, the same magnitude of Fn × s (the Archard’s loading factor) produces the same running in period and the same steady state
period, in other words, the same wear mechanism, in two specific cases: 0.5 N 130 m/1 N 65 m and in 1 N 130 m/2 N 65 m. This last case is shown in Fig. 15 for 90◦ crossing angle. Taking into account that the contact pressure is directly related with the normal force Fn and the contact angle ˛, it could be related the stroke and the contact pressure with the wear behaviour. Considering the contact pressures used in these tests, it could be defined a relation Pav × s which could explain the same wear mechanism for these specific tests. This relation is presented in Eq. (15): Psm × sgt 1.59 Pgt × ssm
(15)
Fig. 15. Wear results for different contact angles and 2 different initial average contact pressures and strokes: (a) total linear wear; (b) total volumetric wear; (c) energy specific wear resistance; (d) coefficient of wear for test series 1.
A. Cruzado et al. / Wear 273 (2011) 60–69
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with Pgt = greater contact pressure (3200 Mpa); ssm = smaller stroke (65 m); Psm = smaller contact pressure (2500 Mpa) and sgt = greater stroke (130 m). After this it is important to know that the wear behaviour of both periods (running in period and steady state period) not only depends on the contact pressure but it depends on the relation of contact pressure–stroke.
under the Universidad Empresa programme in the frame of the SIVICA project (Ref. UE2009-5) as well as from European Commission in the frame of the ERASMUS programme and from BAM Federal Institute for Materials Research and Testing is gratefully acknowledged.
4. Summary and conclusions
[1] R.B. Waterhouse, Fretting Fatigue, Applied Science Publishers Ltd., London, 1981. [2] K.K. Schrems, Wear related fatigue in a wire rope failure, Journal of Testing & Evaluation 22 (1994) 490–499. [3] R.B. Waterhouse, Fretting in steel ropes and cable—a review, ASTM Special Technical Publication 1425 (2002) 3–14. [4] R.B. Waterhouse, D.E. Taylor, Fretting fatigue in steel ropes, Lubrication Engineering 27 (1971) 123–127. [5] M.A. Urchegui, M. Hartelt, D. Klaffke, X. Gómez, Laboratory fretting tests with thin wire specimens, Tribotest 13 (2007) 67–81. [6] A. Cruzado, M. Hartelt, R. Wäsche, M.A. Urchegui, X. Gómez, Fretting wear of thin steel wires. Part 1: influence of contact pressure, Wear 268 (2010) 1409–1416. [7] R. Wäsche, M. Hartelt, Wear testing with crossed cylinders—comparison of methods, in: W.J. Bartz (Ed.), Proceedings 16th International Colloquium on Tribology, Technische Akademie Esslingen, Ostfildern, January 15–17, 2008. [8] D. Klaffke, On the influence of test parameters on friction and wear of ceramics in oscillating sliding contacts, TriboTest 1 (1995) 311–320. [9] M.A. Urchegui, W. Tato, X. Gómez, Wear evolution in a stranded rope subjected to cyclic bending, Journal of Materials Engineering and Performance 17 (2007) 550–560. [10] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985. [11] S. Fouvry, Etude quantitative des dégradations en fretting [Quantitative aspects of fretting damages], PhD Thesis, 97–04, Ecole Central de Lyon, Ecully, France, 1997. [12] D. Klaffke, Towards a tribological reference test-fretting test? TriboTest 12 (2006) 11. [13] D. Klaffke, Fretting wear of ceramics, Tribology International 22 (1989) 89–101. [14] M.A. Urchegui, X. Gómez, W. Tato, A method for evaluating fretting wear scars in thin steel roping wires based on confocal imaging profilometry, Journal of Testing and Evaluation 35 (2007) 357–363. [15] S. Fouvry, Shakedown analysis and fretting wear response under gross slip condition, Wear 251 (2001) 1320–1331. [16] H. Kato, k. Komai, Tribofilm formation and mild wear by tribo-sintering of nanometer-sized oxide particles on rubbing steel surfaces, Wear 262 (2007) 36–41. [17] S. Fouvry, T. Liskiewicz, C. Paulin, A global-local wear approach to quantify the contact endurance under reciprocating-fretting sliding conditions, Wear 263 (2007) 518–531.
Oscillating sliding tests were carried out on thin steel wires under fretting conditions using the crossed cylinders contact geometry. The main parameters were the crossing angle and the contact pressure. The crossing angle was varied between 30◦ and 90◦ . Two different types of test were carried out. In the first test series the normal load was kept constant at 1 N which leads to different initial contact pressures according to the applied crossing angle. In the second test series the normal load was adjusted in that way that the initial contact pressure is largely kept constant at all crossing angles. The results show that the generated wear volume is mainly dependent on the normal load. The consideration of the accumulated dissipated energy leads to an energy specific wear resistance as a measure of the wear intensity. The results may be understood assuming two different wear periods namely a running-in period and a steady state period with two different wear coefficients. The transition of these two periods could be attributed to the formation of oxide protective layers. A varying length of the running-in period due to a changing contact pressure would then result in a different wear coefficient, as seen in test series 1. A constant ratio between the running in process and the following steady state process due to a constant contact pressure would then explain the constant wear coefficients in test series 2. Finally it is important to remark that the wear behaviour of both periods depends on the relation contact pressure–stroke. Acknowledgements The authors would like to thank Christine Neumann for technical assistance. The financial support from Basque Government
References