Analysis of frictional behavior of electrodeposited coatings against spherical counterfaces.
Keywords Cathodic electrodeposited coating, Sliding friction coefficient, Steel, Ceramics
Electrodeposition is applied to automotive components for the purpose of increasing corrosion resistance. (1-3) Particularly, epoxy-based cathodic electrodeposited coatings are typically used for automotive seat sliding rails. A ball or a solid cylinder located between coated rails enables linear motion of a seat. At Hertzian contact between a ball and a coated rail, semielliptic pressure distribution is observed. (4,5) Maximum contact pressure and maximum shear stress are determined based on the mechanical properties of the contacting materials (i.e., a ball and a coated rail). Initially, a ball comes into contact with an electrodeposited coating layer on a rail. After an electrodeposited coating deteriorates, a ball encounters the substrate of a rail; in this case, contact pressure is higher than that found at an initial contact condition. In addition, contact between a ball and the substrate causes squeaking noise in the seat sliding rails. (6,7) For this reason, tribological performance of an electrodeposited coating is of great importance in the design of seat sliding rails.
The kinetic friction coefficient is a useful indicator for describing tribological performance of a solid lubricant coating. (8) The friction coefficient of a solid lubricant coating typically starts at a low value. (9,10) After a "running-in" period, the friction coefficient remains almost steady (secondary stage). Finally, the friction coefficient increases, since the substrate appearing partially at contact becomes larger and larger (tertiary stage). A test with a solid lubricant coating is terminated when the friction coefficient comes to a critical value (e.g., the friction coefficient at metal-to-metal contact). It was identified from the literature (11) that the friction coefficient growth rate of a coated system at the tertiary stage is associated with the amount of substrate appearing on the contact surface.
In order to predict friction behavior of a low-friction solid lubricant coating, friction coefficient evolution needs to be described with an appropriate law. The friction coefficient growth rate of the coating was expressed as a function of the friction coefficient itself. (12) Two parameters, defined as the damage rate constant and the damage exponent, determined the evolution law of fretting wear damage. It was identified that the damage rate constant was associated with surface roughness. Under unidirectional sliding, friction coefficient evolutions of coated systems were described with exponential, linear or logarithmic forms. (13) It was observed that the damage rate constant was dependent upon applied load. The damage exponent for an exponential form was close to unity, while the exponent for a linear form was close to zero. However, experimental factors associated with the damage exponent are unknown.
In this study, epoxy-based electrodeposited coatings were tested against various metallic and ceramic balls. Ceramics are known to maintain good antifriction performance and have high compressive strength, thereby being used for artificial hip joints subjected to sliding and compressive loading. (14,15) The kinetic friction coefficient was measured and analyzed. The relation between ball hardness and the friction coefficient growth rate was investigated.
Reciprocal linear sliding tester
Figure 1 shows the schematic illustration of a reciprocal linear sliding test machine. The test machine comprised a linear stage, a rigid arm, dead weights, a ball holder, a load cell, and a laser displacement sensor. The carriage of the linear stage (PImiCos GmbH, LS-110, max. travel range of 26 mm) enables horizontal reciprocating motion of a flat specimen. A [PHI]5-mm ball was clamped by a ball holder made of mild steel. A ball holder was allowed to move vertically in a rigid arm. Normal force was applied to the contact area between a ball and a flat specimen by dead weights. A 1.25 kN load cell, connected to a rigid arm, measured cyclic frictional force occurring at the contact. A laser displacement sensor (Keyence LK-081, a resolution of 0.003 mm and a linearity of [+ or -] 0.1%) measured the horizontal displacement of the carriage in the linear stage during the test. The frictional force and the horizontal displacement were recorded. A force-displacement loop was determined after each cycle. In addition, the Coulomb friction coefficient was computed; in this study, the friction coefficient was determined as the ratio of the maximum frictional force to the normal force after each cycle. Finally, a friction coefficient evolution was plotted for each test.
Materials and test condition
A solid coating layer was deposited on a cold-rolled high-strength steel plate by a cathodic electrodeposition process. (The main resin backbone was an epoxy resin with a crosslinker of blocked aromatic isocyanates.) Initial coating thickness ranged from 0.02 to 0.03 mm (provided by the manufacturer). Figure 2 shows the micrograph of the cross section of a specimen captured by an optical microscopy with a ruler. A specimen was obtained from an actual rail by a wire-cut electrical discharge machine. The micrograph shows an initial coating thickness similar to those offered by the manufacturer.
Balls were made of steels (AISI 52100, SUS316L, and AISI 1010) and ceramics (Zr[O.sub.2] and [Si.sub.3][N.sub.4]). A conventional ball (AISI 52100 steel) for automotive seat sliding rails is 5 mm in diameter. Thus, in this study, balls with a diameter of 5 mm and an arithmetic average surface roughness ([R.sub.a]) of 0.025 [micro]m were used. Tables 1 and 2 show the chemical compositions of the steel and ceramic balls selected for reciprocal sliding testing. The mechanical properties of the balls are presented in Table 3.
In order to duplicate the contact situation similar to that found in automotive sliding rails, a normal force of 49 N was applied to the contact area between a ball and a flat specimen. It was assumed that a loaded seat was about 80 kgf in weight and it contained 16 balls. In this study, the imposed frequency and relative displacement between a ball and a specimen were 1 Hz and 1 mm, respectively. All tests were carried out at room temperature (22-24[degrees]C).
Results and discussion
Ball-on-flat tests were conducted with electrodeposited coatings at a normal force of 49 N, an imposed displacement of 1 mm, and a frequency of 1 Hz. Tests were terminated when the friction coefficient reached about 0.5.
Figure 3 shows the friction coefficient evolutions of electrodeposited coatings against SUS316L, AISI 1010, A1SI 52100, [Si.sub.3][N.sub.4], and Zr[O.sub.2] balls. Two tests were employed with each ball. Initial friction coefficient values for all balls ranged from 0.06 to 0.14.
Following a rapid increase, the friction coefficient became stable (secondary stage). In this stage, the coating progressively deteriorated as shown in Figs. 4a and 4b. The friction coefficient at a steady state ranged from 0.2 to 0.3, and there was no significant difference among steady friction coefficients of the chosen counterparts. This stage remained until the substrate appeared on the contact surface. The period of a steady state varied according to the counterpart material. Zr[O.sub.2] balls maintain the longest steady state on an electrodeposited coating among the chosen balls. After steady-state sliding, the friction coefficient showed a strong increase up to 0.5 (tertiary stage); at the end of steady-state sliding, substrate partially appeared at the contact surface as exhibited in Fig. 4b. At a friction coefficient of 0.5, the coating layer was completely removed and a rough substrate surface was observed as shown in Fig. 4c. It was identified that the friction coefficient of the electrodeposited coating against Zr[O.sub.2] ball reached 0.5 after 1150 cycles. Meanwhile, the friction coefficient of the coating against SUS316L came to 0.5 after 348 cycles as shown in Fig. 5.
In order to describe the variation of the friction coefficient, a form of the Kachanov-type damage law was used. (12) In the Kachanov-type damage law, a measure of damage was proposed. In this study, a measure of damage was defined as the Coulomb friction coefficient; that is, a nondamaged state is associated with the friction coefficient at the steady-state sliding contact after the running-in period. A fully damaged state is associated with the friction coefficient at metal-to-metal or ceramic-to-metal contact. The relation between the friction coefficient (/) and the number of cycle (A) is expressed as
df/dN = C x [f.sup.n], (1)
where C is the damage rate constant and n is the damage exponent.
It was found from the literature (12) that the parameter C was related to surface roughness and normal force. Meanwhile, the damage exponent was associated with coating material. (13,16)
For determining the parameters C and n, the following procedure was
employed. First, the measured friction coefficient (f) was fitted with a power-law function as presented in Appendix 1. The derivative of the friction coefficient, df/dN, was then computed with a fitted curve. Finally, df/dN versus f was plotted on a bilogarithmic scale. On the plot, a straight line appeared, meaning that the evolution of the friction coefficient obeyed equation (1). The parameters C and n in equation (1) were determined on the evolution curve.
Figures 6, 7, 8, 9, and 10 illustrate the relation between the friction coefficient growth rate and the friction coefficient. Markers came from the curve fit shown in Appendix 1. Reported quality of fit ([R.sup.2]) in the figures shows that a function for curve fitting offered an adequate description within the range of 0.25-0.5 in friction coefficient. It was identified from plots that the damage rate constant (C) was similar without regard to ball material. Controlled initial surface roughness of a ball might be attributed to similarity among the damage rate constants (C). Meanwhile, the damage exponent (n) varied with respect to a ball. The damage exponent (n) in the plots tends to increase with the increase of ball hardness as shown in Fig. 11.
In this study, various balls were used with the same geometry. Elastic modulus and Poisson's ratio of a ball have an influence on contact pressure. Semielliptic pressure distribution is observed at Hertzian contact between a ball and a steel plate. Based on the mechanical properties of the balls given in Table 3, maximum contact pressure in semielliptic pressure distribution can be determined. Meanwhile, one might consider the number of cycles at a friction coefficient of 0.27 or 0.5 as the durability of an electrodeposited coating. Figure 12 shows the relation between the durability of the coating and the maximum contact pressure calculated with Hertzian contact theory. It was identified that durability of the electrodeposited coating increased with increasing the maximum contact pressure up to 2650 MPa. Meanwhile, when the maximum contact pressure is greater than 2650 MPa, it is difficult to identify the apparent relation between durability of the coating and the maximum contact pressure due to lack of experimental data.
The proposed analysis method is useful for describing the friction behavior of electrodeposited coatings. In addition, it allows quantifying the influence of friction behavior resulting from various experimental factors. Meanwhile, in this study, the growth rate of the friction coefficient was described with a power-law form. Thus, further studies need to investigate the reason that the friction coefficient at the tertiary stage evolves in a power-law form. In addition, observation of morphological change is useful for understanding the transition of the friction coefficient. Thus, additional work should include the observation of morphological change in a coating layer and in the substrate. For the purpose of identifying the apparent relation between durability of the coating and the maximum contact pressure, it is necessary to conduct further tests with various balls.
In this article, ball-on-flat tests were conducted with an electrodeposited coating against various balls. Experimental conditions were similar to those found on automotive seat sliding rails. The following conclusions were drawn:
* An electrodeposited coating against a zirconia ball maintains the longest endurance life among the chosen balls in terms of the friction coefficient.
* The friction coefficient growth rate of an electrodeposited coating can be expressed as a power-law function of the friction coefficient. It was identified that the damage exponent in a power-law form was associated with ball hardness. The damage exponent increased with the increase of ball hardness.
Further work needs to investigate the reason that the friction coefficient at the tertiary stage evolves in a power-law form. In addition, observation of morphological change is useful for understanding the transition of the friction coefficient. Thus, further work needs to include the observation of morphological change in a coating layer and in the substrate. For the purpose of identifying the apparent relation between durability of the coating and the maximum contact pressure, it is necessary to conduct further tests with various balls.
K. Kim ([mail])
School of Aerospace and Mechanical Engineering, Korea Aerospace University, 76 Hanggongdaehang-ro, Deogyang-gu, Goyang-si, Gyeonggi-do 412-791, Republic of Korea
Power-law from for curve fitting: f = [f.sub.0] + a x [N.sup.b]. All data except initial friction coefficient were used for curve fitting.
Appendix 1 Power-law form for curve fitting: f = [f.sub.0] + a x [N.sup.b]. All data except initial friction coefficient were used for curve fitting. Ball material Test No. [f.sub.0] a SUS316L 1 0.242 7.360 x [10.sup.-9] 2 0.237 5.192 x [10.sup.-8] AISI 1010 1 0.247 1.214 x [10.sup.-12] 2 0.234 6.144 x [10.sup.-19] AISI 52100 1 0.260 6.714 x [10.sup.-19] 2 0.246 3.690 x [10.sup.-24] [Si.sub.3][N.sub.4] 1 0.257 6.745 x [10.sup.-19] 2 0.245 3.569 x [10.sup.-15] Zr[O.sub.2] 1 0.260 2.943 x [10.sup.-14] 2 0.261 3.277 x [10.sup.-16] Ball material Test No. b [R.sup.2] SUS316L 1 2.987 0.987 2 2.637 0.981 AISI 1010 1 4.037 0.983 2 6.209 0.893 AISI 52100 1 5.934 0.988 2 7.800 0.937 [Si.sub.3][N.sub.4] 1 5.881 0.967 2 4.649 0.938 Zr[O.sub.2] 1 4.239 0.981 2 4.844 0.992
Determination of maximum contact pressure ([P.sub.0]) between a ball and a plate with Hertz contact theory
[P.sub.0] = [(6 x F x [E.sup.*2]/[[pi].sup.3] x [R.sup.2]).sup.1/3],
where 1/[E.sup.*] = 1 - [v.sup.2.sub.1]/[E.sub.1] + 1 - [v.sup.2.sub.2]/[E.sub.2].
F is the normal force, R is the radius of a ball, [E.sub.1] and [v.sub.1] are the elastic modulus and Poisson's ratio of a ball, and [E.sub.2] and [v.sub.2] are the elastic modulus and Poisson's ratio of a plate, respectively.
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Table 1: Chemical composition (wt%) of commercial steel balls Steel C Si Mn AISI 52100 0.95-1.10 0.15-0.35 0.05 SUS316L 0.03 1.00 2.00 AISI 1010 0.08-0.13 0.15-0.35 0.3-0.6 Steel P S Cr Mo AISI 52100 0.025 0.025 1.3-1.6 0.08 SUS316L 0.045 0.03 16-18 2.0-3.0 AISI 1010 0.03 0.03 -- -- Table 2: Chemical composition (wt%) of commercial ceramic balls Ceramic Zr[O.sub.2] [Y.sub.2][O.sub.3] Zr[O.sub.2] 94.8 5.2 [Si.sub.3][N.sub.4] Ceramic [Si.sub.3][N.sub.4] Y Al Ti Zr[O.sub.2] [Si.sub.3][N.sub.4] 90.0-92.5 3.0-4.0 3.5-4.5 1.0-1.5 Table 3: Mechanical properties of balls provided by the manufacturers Property SUS316L AISI 1010 AISI 52100 Hardness (HRC) 11 58-60 60-63 Elastic modulus (GPa) 190-193 190-210 190-210 Poisson's ratio 0.27-0.3 0.27-0.3 0.27-0.3 Property Zr[O.sub.2] [Si.sub.3][N.sub.4] Hardness (HRC) 70 75-80 Elastic modulus (GPa) 200-210 310-320 Poisson's ratio 0.23-0.3 0.26-0.27 Fig. 5: Endurance lives of an electrodeposited coating against various balls SUS316L 348 AISI1010 670 AISI52100 896 [Si.sub.3][N.sub.4] 953 Zr[O.sub.2] 1,150
Please note: Some tables or figures were omitted from this article.
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|Publication:||Journal of Coatings Technology and Research|
|Date:||May 1, 2015|
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