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Oct 8, 2014 - p-hydroxybenzoic acid and their copolyesters. In: 100 ? Years of. Plastics. Leo Baekeland and Beyond, vol. 1080. ACS Symposium. Series, vol.
Tribol Lett (2014) 56:387–395 DOI 10.1007/s11249-014-0416-y

ORIGINAL PAPER

Mechanical and Tribological Properties of Ekonol Blends as Frictional Materials of Ultrasonic Motors Jianjun Qu • Yanhu Zhang • Xiu Tian Wenfeng Guo



Received: 16 July 2014 / Accepted: 15 September 2014 / Published online: 8 October 2014 Ó Springer Science+Business Media New York 2014

Abstract While high friction coefficients and good wear resistance are antagonistic properties of most materials, these properties are expected to promote excellent torquespeed characteristics and extend the life span of ultrasonic motors. Blending is an accepted technique for modifying tribological applications. p-Hydroxybenzoic acid polymer (Ekonol) blends with different compositions, and proportions were prepared through mechanical blending. Poly(tetrafluoroethylene) (PTFE), poly(etheretherketone), and poly(phylenesulfide) (PPS) were selected as dispersed phases. The mechanical properties of the blends were investigated, and their tribological performance was tested using a block-on-ring wear meter. The worn surfaces of Ekonol blends were observed using a scanning electron microscope to elucidate the relevant wear mechanisms. Results showed that the dispersed phases have distinct effects on the impact strength and hardness, as well as friction coefficient and wear rate, of the blends. Curves of hardness and friction coefficient versus the dispersed phase content showed apparent similarities, which indicates that hardness influences the friction of polymer blends in contact with carbon steel. Worn tracks on the surfaces of different polymer materials showed that the dominant wear mechanism transforms from fatigue and abrasion into adhesion with the addition of a dispersed phase; delamination was observed in the transfer films, especially those formed by the Ekonol/PTFE and Ekonol/PPS blends. J. Qu (&)  Y. Zhang  W. Guo School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China e-mail: [email protected] X. Tian Beijing Aerospace Control Instrument Research Institute, Beijing 100854, China

Keywords Blends  Polymer  Mechanical properties  Unlubricated friction  Wear mechanisms

1 Introduction Frictional materials exert an important function in ultrasonic motors (USMs), and excellent mechanical properties and tribological performances are desired for friction materials [1]. Elastic modulus [2] and hardness of frictional materials [3] affect both output characteristics and frictional noise [4] of USMs. As USMs are driven by friction, high-efficiency motors require adequately high friction coefficients. Long service lifetimes and good wear resistance of frictional materials are also essential for USMs [5]. The properties of frictional materials of USMs are clearly different from those used in ordinary tribological materials, such as gears, cams, and bearings, where the coefficient of friction and wear rate are expected to be very low. Thus, common frictional materials cannot be used in USM unless they provide high friction coefficients and low wear rates. The poor performances in the hardness and wear resistance, bonding strength, and assembly of commercially resins [6] and plastics [7], restraint themselves as friction materials of USMs. p-Hydroxybenzoic acid polymer (Ekonol) is a linear thermoplastic polymer widely applied in chemical and energy materials because of its excellent performance against heat and oxidation and high thermal stability and chemical resistance [8, 9]. Ekonol is self-lubricating and provides excellent friction and wear properties under extreme conditions [10]. Unfortunately, Ekonol is a highly crystalline polymer that is extremely brittle and difficult to process. In our previous study [11], Ekonol composites showed larger torques than poly(tetrafluoroethylene)

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various materials. We hypothesized that blending can improve the mechanical properties and modify the dominant wear mechanism of Ekonol blends. This study focuses on the mechanical properties (impact resistance and hardness) and tribological performance of several developed polymer blends. Ekonol/PTFE, Ekonol/PEEK, and Ekonol/ PPS blends with varying amounts of the dispersed phase (0–30 wt%) were synthesized and compared. The resultant blends may be used as potential alternatives for frictional materials of USMs.

Table 1 Molecular structure of the polymers Polymer

Molecular structure

O Ekonol

O

*C

n

O PEEK

O

O

C

S

PPS

PTFE

F

F

*C

C

F

F

n

n

2 Experimental Details 2.1 Materials

n

(PTFE) composites under high USM speeds. PTFE [12–14] is a solid lubricant with an unusually high wear rate and creep deformation and is used widely in tribological applications. Poly(phenylenesulfide) (PPS) and poly(etheretherketone) (PEEK) are semi-crystalline thermoplastic polymers with superior mechanical strength and thermal stability; thus, these materials are promising frictional materials [15]. Bijwe et al. [16] reported that excellent mechanical and tribological properties of PEEK-PTFE blends in adhesive and fretting wear modes can be achieved by optimizing the compositions of the blends. Yamamoto and Takashima [15] investigated the tribological performances of PEEK and PPS under water lubrication and found that PPS can form a transfer film on the mating steel surface better than PEEK can. As well, PEEK use during coldcrystallization [17] contributes to the resultant synergistic behavior of ternary PEEK/PEI/TLCP blends, thereby allowing sliding and good wear behavior at temperatures well in excess of the Tg of the constituent phases. Polymer technology generally varies, producing singlephase materials to diverse combinations of polymers, additives, and reinforcements. Blending [18, 19] is an effective and economical approach for providing materials with rich properties. Synergistic and additive effects [20] are often cited for widening the range of properties of

The neat polymers used in this study included EkonolÒ, PEEK, PPS, and PTFE, and their structures are shown in Table 1; the feedstock powders applied to the polymer blends are listed in Table 2. The feedstock powders were blended with the polymers according to preselected proportions. 2.2 Polymer Blend Preparation The Ekonol blends were prepared by mixing, compression molding, and then sintering (Fig. 1). The Ekonol contents, as the main mixed phase (matrix), were changed from 70 to 100 wt%. PTFE, PEEK, and PPS were used as dispersed phases and applied as proportions of 5, 10, 20, and 30 wt%. 2.3 Procedure The Charpy impact test was performed according to GB/T 1043.1-2008 (ISO 179-1:2000) with an XJJ-5 impact tester at room temperature (20 °C ± 2 °C). Two Charpy tests, namely the notched Charpy test (for Ekonol/PTFE and Ekonol/PEEK) and the unnotched Charpy test (for Ekonol/ PPS), were separately conducted to investigate the effects of stress concentration on the polymer blends. The hardness values of the polymer blends were determined according to GB/T 2411-2008 with a Shore D TH210 hardness tester.

Table 2 Details of feedstock powders employed in this study Grain size (lm)

Real density (g/mm3)

Composition (wt%)

Source

Ekonol

15

1.45

Matrix

BlueStar Chengrand R&D Institute, Nanjing

PTFE

25

2.15

PEEK

20

1.27

5 Co, 10 Co, 20 Co, 30 Co, separately, balance Ekonol

Special Engineering Plastic Research Institute Co., Ltd. Changchun

PPS

37

1.36

Powder type

123

Special New Materials Co., Ltd. Deyang

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Powder

389

Drying

Weighing



Sintering

Cold moulding

Cooling

Dressing

h i1=2 R2 arcsin½B=ð2RÞ  B2 R2  ðB=2Þ2 2pRxtF

b

ð2Þ

where w is the wear rate of the polymer blend, R is the external radius of the ring, B is the wear width on the contact zone, b is the sample width, F is the normal force applied on the friction pair, x is the speed of ring, and t is the testing time. In this study, each test was performed thrice to minimize measurement errors. Average values of the friction coefficient and wear rate are reported. The polymer blocks were molded, and the test surface was smoothened with abrasive paper #1200, after which a final polishing of a roughness (Ra) of 0.2 lm was performed. After cutting the steel rings, the test surfaces of rings were smoothened with abrasive paper #600 and #1000 (around a Ra of 0.4 lm). After the wear tests, the worn surfaces of the polymer specimens (and their blends) were examined with scanning electron microscopy (SEM) using a Hitachi S-520 electron microscope operated at 20 kV. The worn surfaces of specimens were sputter coated with gold before viewing under the microscope.

Mixing

Testing

Fig. 1 Flow chart of the sample preparation procedure

3 Results and Discussion Fig. 2 Schematic diagram of contact couples for the M-200 tribometer (in mm)

3.1 Mechanical Properties 3.1.1 Impact strength

Wear tests were conducted on a block-on-ring wear tester apparatus (M-200 tester, Materials Testers Company, Xuan-hua, China) according to GB 3960-83. Figure 2 shows a schematic diagram of the frictional couple. The blocks were made of polymer blends, and the ring was made of plain carbon steel with a hardness of HRC 43 ± 2. In each test, the polymer blend blocks were placed against the rotational steel ring under dry conditions in air at room temperature with a relative humidity of 40 ± 5 %. The rotational speed of the ring was maintained at 200 r/min, and a total sliding distance of about 754 m was set for each test. The normal load was set to 100 N. The ring was dressed prior to the each test to remove debris from previous tests and ensure the reproducibility of test conditions. The friction coefficient and wear rate were determined and recorded using the aforementioned rig. Friction torques (T) were periodically recorded, and the friction coefficient was calculated as follows: l¼

T FR

ð1Þ

The wear rate (w, mm3/Nm) reported in this study was calculated according to Eq. (2).

The wear on sliding surfaces may include plastic deformation, subsurface cracks, and void nucleation. The combined effects of these defects may be represented by the macroscopic mechanical properties of the material to some extent. Figure 3 shows the impact strength and shore hardness of the A/B polymer blends (A, Ekonol; B, dispersed phase). Figure 3 shows the influence of polymer content on the impact strength of the Ekonol blends with various dispersed

Fig. 3 Relationship between impact strength and dispersed phase content in the polymer blends. Bidirectional arrows indicate extreme variations in impact strengths after blending. ‘‘?’’ indicates improvements in impact strength

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phases (PTFE, PEEK, and PPS). The impact strength of Ekonol/PTFE showed a wave-like change with increasing PTFE content, and its value reached a minimum (1.091 kJ m-2) when the PTFE content was increased to 20 wt%. The impact strength of the Ekonol/PEEK blend initially increased and then decreased with increasing PEEK content. In contrast to the Ekonol/PTFE blend, the Ekonol/ PEEK blend showed maximum impact strength when the PEEK content was about 20 wt%. The influence of PPS on the impact strength of Ekonol/PPS blend was unique from those in the first two blends. No significant change in impact strength was observed until the PPS content reached a critical value of 10 wt%, after which the impact strength of the Ekonol/PPS blend linearly increased with increasing PPS content. 3.1.2 Shore hardness Figure 4 shows the results of the shore hardness tests. The shore hardness test predicts the influence of increasing PTFE, PEEK, or PPS contents on the Ekonol blends. A distinct difference in shore hardness was observed among the blends with various dispersed phases. First, with increasing PTFE content, the hardness of the Ekonol/PTFE blend linearly decreased until the PTFE content reached 10 wt%. Further increases in PTFE content showed no significant effect on the shore hardness of the Ekonol/PTFE blend. Increasing the PEEK content from 5 to 10 wt% did not significantly change the shore hardness of the Ekonol/ PEEK blend. At a PEEK content of 10 wt%; however, the shore hardness of the Ekonol/PEEK blend considerably increased. Further increases in PEEK content did not show substantial effects on the hardness of the Ekonol/PEEK blend, although a slight decrease was observed. The hardness of the Ekonol/PPS blend significantly increased initially with increasing PPS content and then gradually stabilized.

Fig. 4 Relationship between shore hardness and dispersed phase content in the three polymer blends. Bidirectional arrows indicate extreme variations in shore hardness after blending. ‘‘?’’ and ‘‘-’’, respectively, indicate increases and decreases in Ekonol blends hardness

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3.2 Tribological Properties 3.2.1 Friction Coefficient Figure 5 shows the friction coefficients of the A/B Ekonol blends with different contents of B (PTFE, PEEK, and PPS). As the PTFE content increased, the friction coefficient of the Ekonol/PTFE blend gradually decreased, reaching a minimum at 10 wt% PTFE. Further increases in PTFE content showed no significant effect in the final friction coefficient of the blend. At PEEK contents \5 wt%, the friction coefficient of the Ekonol/PEEK blend was nearly equal that of pure Ekonol. When the PEEK content reached 10 wt%, the friction coefficient of this blend slightly increased from 0.287 to 0.309. Further increases in PEEK content up to 20 wt% did not cause the friction coefficient of the Ekonol/ PEEK blend to vary significantly. In the Ekonol/PPS blend, the average friction coefficient varied with increasing PPS content. As the PPS content increased, the friction coefficient of the Ekonol/PPS blend evidently increased (0.463). Further increases in PPS content to 10 wt% resulted in an initial slight increase in friction coefficient followed by gradual stabilization. In contrast to the friction coefficient of the Ekonol/PEEK blend, the friction coefficient of the Ekonol/PPS blend rapidly increased initially with increasing PPS content and then eventually stabilized. 3.2.2 Wear Rate Figure 6 shows the general trend of the wear rate of the Ekonol/PTFE blend. The wear volume of the blend increased with increasing PTFE content, which suggests that addition of PTFE does not improve the wear resistance of the Ekonol/PTFE blend. By contrast, as the PEEK

Fig. 5 Relationship between friction coefficient and dispersed phase content in the three polymer blends. Load: 100 N; time: 30 min. Bidirectional arrows indicate absolute increments of the friction coefficient of the Ekonol blends in contact with carbon steel; ‘‘?’’ and ‘‘-’’, respectively, show increased and decreases in friction coefficient

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curves above, the wear rates of Ekonol blends with various dispersed phases showed no dependence on the friction coefficient. Thus, we conclude that the dominant wear mechanism of Ekonol blends in contact with carbon steel is not simply frictional wear; other mechanisms may also take place. Specifically, the friction coefficients and wear rates obtained may predict the predominant wear mechanisms and describe how the composition and morphology of polymer blends affect tribological performance. 3.2.3 Morphology of Wear Surfaces Fig. 6 Variation in wear rates of the polymer blends with increasing dispersed phase contents. Load: 100 N; time: 30 min. Bidirectional arrows indicate maximum increments of the wear rate of the Ekonol blends in contact with carbon steel. ‘‘?’’ and ‘‘-’’, respectively, indicate increases and decreases in wear rate

content increased, the wear loss of the Ekonol/PEEK blend linearly decreased, reaching a minimum value at 20 wt% PEEK. Further increases in PEEK content increased the amount of wear, which remained less than that of the pure Ekonol matrix. The wear resistance of the Ekonol/PEEK and Ekonol/PPS blends showed similar trends. The wear rate of the Ekonol/PPS blend reached minimum values when the polymer blend contained 5 wt% PPS. Based on the results obtained, we conclude that the wear rate sharply increases with increasing friction coefficient. Interestingly, the wear rate of the Ekonol/PPS and Ekonol/ PEEK blends appeared to increase with increasing dispersed phase content. Referring to the friction coefficient Fig. 7 SEM micrographs of the worn surfaces of: a Ekonol, b Ekonol/PTFE (80/20), c Ekonol/PTFE (50/50), and d Ekonol/PTFE (20/80). Arrows indicate the sliding direction. Load: 100 N; time: 30 min

The presence of PTFE in the Ekonol/PTFE blend caused deterioration of its friction coefficient and wear resistance. As such, the Ekonol/PTFE blend was not extensively investigated beyond the SEM analysis. Figure 7 shows the worn surfaces of the Ekonol/PTFE blend under drying sliding. Under sliding friction, concomitant tangential stresses produce compressive stresses parallel to the sliding direction of the contact as well as corresponding tensile stresses along the rail of the contact [21]. Pure Ekonol is brittle and prone to cracking and peeling under compressive and tensile stresses. Fatigue cracks and plowing tracks may also be observed on the worn surface. Even at low PTFE contents, microcracks were still observed on the worn surface of the blend and crushing appeared along the edge of plowing. Further increases in PTFE content yielded smoother, worn surfaces, although microcracking and transfer tracks were still observed.

(a)

(b)

(c)

(d)

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392 Fig. 8 SEM micrographs of the worn surfaces of: a Ekonol, b Ekonol/PEEK (95/5), c Ekonol/PEEK (90/10), and d Ekonol/PEEK (70/30). Arrows indicate the sliding direction

Comparison of the SEM photos of Ekonol/PTFE with different PTFE contents shows that the wear surface shows more regular and thinner peeling substructures as the PTFE content increases. The characteristics of less brittleness and moderate peeling in this blend indicate that brittleness depends on PTFE content. As the PTFE content is increased, the Ekonol matrix gradually becomes more flexible to a substantial extent. The predominant wear mechanism of Ekonol/PTFE appeared to transform from fatigue peeling and mechanical plowing into adhesive wear. The hard and brittle Ekonol matrix is highly prone to impact and fatigue wear, while the soft PTFE is easy to disperse to form transfer films. The presence of low sliding resistance between molecular chains promotes chain slippage between linear chains. Thus, the hard Ekonol matrix presents loading actions and the soft PTFE component forms the so-called transfer films, thereby preventing hardto-hard contact between the metal and the Ekonol blends. Figure 8 shows the worn surfaces of Ekonol/PEEK blends. Slight changes in PEEK content can markedly alter the wear behavior of the Ekonol/PEEK blend. For instance, the worn surface of the Ekonol/PEEK (95/5) blend shows a smoother surface than the pure Ekonol matrix and presents fewer scratches and slight plowing traces. PEEK also has a toughening effect on Ekonol. As the PEEK content was increased, several microvoids appeared on the worn surface of the Ekonol/PEEK blend. We previously speculated that these microvoids are caused by several thermal controlling defects. One of these defects is involves surface defects

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(a)

(b)

(c)

(d)

caused by uneven melt flow during the sintering process; another is frictional heat from the interface brought about by the low thermal conductivity of the polymer blend. Progressive cavitation erosion accompanied by local plastic deformation is yet another defect that may arise from the so-called isolated stress concentrations and hot spots, which result from the absence of gradual transitions in heat and stress during friction. Compared with pure Ekonol, addition of PPS appeared to reduce the plowing component of friction, resulting in a flatter worn surface (Fig. 9). In the Ekonol/PPS (95/5) blend, the worn surface was smooth and non-plowed traces were observed. Combining our data on wear rate, we conclude that PPS improves the wear resistance of the Ekonol blend by forming transfer films. The micrographs show that delamination occurs in the Ekonol/PPS blend but is aggravated with increasing PPS content. Laminar particles resulting from delamination form the transfer films in the contact region between the polymer blend and carbon steel surfaces. 3.3 Discussion The impact strength presents an important function in mitigating friction and wear. The Charpy test results show that addition of dispersed phases (PTFE, PEEK, and PPS) to the Ekonol matrix modifies the impact strength of the resulting blend in the unnotched Charpy tests, addition of PPS improved the impact strength of the resultant blend. At

Tribol Lett (2014) 56:387–395 Fig. 9 SEM micrographs of the worn surfaces of: a Ekonol/PPS (95/5), b Ekonol/PPS (85/15), and c Ekonol/PPS (70/30). Arrows indicate the sliding direction. Load: 100 N; time: 30 min

393

(a)

(b)

(c)

low PPS contents, the small number of PPS particles was insufficient to improve the impact strength significantly. In the notched Charpy tests, the impact strength of the Ekonol/PTFE and Ekonol/PEEK blends improved with the increasing dispersed phase content. By increasing the PEEK content to up to 20 wt%, the impact strength also increases. The maximum impact strengths resulting from optimum blend compositions are considerably higher than that of pure Ekonol. The impact strength of the Ekonol/ PTFE blend reached a maximum value when the PTFE content was 30 wt%. In polymer blends, two basic routes of friction and failure resulting in deformation (plastic and/or viscoelastic) and fatigue (cracking and cutting) strongly depend on several factors; these factors include component contents, their miscibility, and their morphologies. Polymer friction in cross-linked structures has been inspected in the microscopic view [22]; results showed that the friction and adhesion forces of non-cross-linked polystyrene decrease significantly by repeated sliding, whereas few changes occur on the cross-linked surface. In the case of PTFE, the lattice braid structure of this component allows its molecules to slide past one another, thereby decreasing friction. Substantial evidence is available to conclude that transfer films exert critical functions in polymer friction [23]. For instance, the transfer films of PTFE have been previously

Fig. 10 Illustration of the interfacial and cohesive wear processes at the stator–rotor interface. Piezoceramic vibrations yield inverse piezoelectric effects, and material points of the elastic stator oscillate along an elliptical orbit, causing the rotor to rotate well. During this process, the stator slides along the contact surface with the rotor and rotates to some extent, thereby causing vibrational deformation. Under normal dynamic contact forces, the soft and viscous rotor (with frictional materials such as polymer composite layers) can be divided into two zones: the interface zone and the adhesive zone. The M-200 tribometer is a typical slide-roll friction-testing rig in which the ring is in contact with the block during operation. While the friction and wear tests were not performed using an actual USM, the tribological performance of the Ekonol blends observed in this work conform to requirements for frictional materials in these motors. Thus, the blends described here may be used in USMs

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Fig. 11 Illustration of improvements in the mechanical properties of the polymer blends. Addition of the dispersed phases altered the mechanical properties of the polymer blends (referring to the data of a single polymer) via three mechanisms, namely the additive effect, the incompatible effect, and the synergistic effect

shown to consist of large, plate-like debris; this finding is confirmed in the present study (see Fig. 10). The formation of transfer films has been shown to considerably prevent substantial increases in the wear rates of PEEK and PPS, similar to findings in other polymers [15]. The wear rate of PEEK (which hardly forms a transfer film) is 6 9 10-5 mm3/Nm, larger than that of PPS (2 9 10-5 mm3/Nm), which forms a transfer film to some extent. In this study, the minimum wear rates of the Ekonol/PEEK and Ekonol/PPS blends were lower than 2 9 10-5 mm3/Nm. As aforementioned, among of the possible patterns of property dependence on blend composition, synergistic effect would put some properties into a valley (optimal minimum) or crest (optimal maximum), but not a monotone variable with the content of dispersed phase (the classification termed ‘‘additive’’ includes a range of values but does not exhibit maxima or minima [20] ), as shown by Fig. 11. We tentatively suggest that synergistic effects have functions in the friction and wear behaviors of the Ekonol/PEEK and Ekonol/PPS blends. For example, chemical bonds existing between the aromatic ring and sulfur atoms may allow PPS to function as a nucleating agent, thereby increasing the crystallinity of Ekonol and providing a hard and highly wear-resistant surface. By contrast, ‘‘additive’’ effects serve an important function in the tribological performance of the Ekonol/ PTFE blend. The friction coefficient curves obtained in this work were similar to those of shore hardness, and the wear rates were inversely proportional to the shore hardness of the polymer blends. Compared with the impact strength test results, the shore hardness appeared to show a more significant influence on the friction coefficient and wear resistance of the blends.

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This paper describes the influence of composition and component content on the mechanical properties (impact strength and shore hardness) and tribological behaviors of Ekonol blends. Considering limitations in space and the author’s knowledge, this paper does not discuss the miscibility and morphologies of the blends described above, although the former is known to depend on thermodynamic and rheological properties and the latter is known to depend on the balance of enthalpy effects. The dependencies are key issues determining the performance of a polymer blend. No single property has yet been identified to clearly dominant the wear mechanisms of blends. Further studies are necessary to identify the mechanism(s) involved in the formation and transport of stratified layers resulting in laminar and/or granular particles.

4 Conclusion The mechanical properties of Ekonol can be improved by blending. Ekonol has a chemical structure similar to that of PPS and PEEK fragments in a linear chain form and may be expected to provide synergistic effects that would endow materials with desirable properties. Both the composition and proportion of the dispersed phase affected the maximum values of Charpy impact strength and shore hardness of the blends. No significant differences between the properties of the polymer blends and pure Ekonol were observed at dispersed phase contents lower than 10 wt%. By increasing the dispersed phase content to 30 wt%, the Ekonol/PTFE and Ekonol/PPS blends yielded maximum impact strengths. The Ekonol/PEEK blend yielded a maximum impact strength at 20 wt% PEEK. Experimental results from our analysis of the Ekonol blends show improvements in tribological performance. The friction coefficients and wear rates of the Ekonol/PPS and Ekonol/PEEK blends were highly affected by the dispersed phase content. The effects of mechanical properties of the polymer blends on their tribological performance were substantial, especially in cases with paradoxical demands on friction and wear. The effects of dispersed phase content on shore hardness and friction coefficient were apparently similar, which indicates that the shore hardness of the Ekonol blends has a critical function in the sliding friction of polymer blends in contact with carbon steel. SEM images of the worn surfaces of the blends show that the dominant wear mechanism transforms from fatigue and abrasive wear to adhesive wear according to the dispersed phase blended with the matrix. Acknowledgments We are grateful to the National Natural Science foundation of China (No: 50975057, 51175104), and the National

Tribol Lett (2014) 56:387–395 Basic Research Program of China (No: 2013CB632305) for providing research funds.

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