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Thermally conductive rubber-based composite friction materials for railroad brakes – Thermal conduction characteristics
COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 67 (2007) 2665–2674 www.elsevier.com/locate/compscitech
Thermally conductive rubber-based composite friction materials for railroad brakes – Thermal conduction characteristics A. Shojaei *, M. Fahimian, B. Derakhshandeh Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran 11365-9465, Iran Received 23 November 2005; received in revised form 13 February 2007; accepted 8 March 2007 Available online 20 March 2007
Abstract This study deals with the thermal conductivity of rubber-based composite friction materials used in railroad vehicles. Based on a commercially available railroad friction material, called here base material (BM), various friction materials containing different thermally conductive fillers (Cu, brass, Al, Al2O3 and talc) are fabricated and then their thermal conductivities are measured at various contents of the fillers. Addition of the thermally conductive fillers causes an increase in thermal conductivity of the friction material from 0.48 up to 5.8 W/m K, depending on the type and content of the filler. In addition, the experimental results reveal that the thermal conductivity of the friction material can be influenced by indirect effects including mainly the shape and size of the filler. Fillers with larger size and platelet shape are more effective in enhancing the thermal conductivity of the friction material. In order to provide an engineering tool to estimate the thermal conductivity of the friction materials, a new semi-empirical model is proposed for multiphase systems based on geometric mean model. In this model, the filler may be regarded thermally conductive or non-conductive. The model is first developed for friction material containing multi-non-conductive fillers and one thermally conductive filler and then is extended to a system containing multi-conductive and non-conductive fillers. The agreement between model predictions and experimental measurements is satisfactory. 2007 Elsevier Ltd. All rights reserved. Keywords: A. Polymer–matrix composites (PMCs); B. Friction; B. Thermal property; B. Thermally conductive fillers
1. Introduction Polymer-based composite friction materials are widely used in frictional brake systems of many vehicles, particularly in brake systems of railroad vehicles due to numerous advantages of this kind of materials such as good braking performance, long life, low braking noise and light weight [1]. Friction, wear and physical properties of such friction materials are governed by different ingredients in formulation of the composite (typically up to 20 different ingredients). Generally speaking, these ingredients can be categorized into primary groups based on their expected functions including binder or polymer matrix, friction modifiers, reinforcements and fillers [2–4]. *
Corresponding author. Tel./fax: +98 21 66164586; fax: +98 21 66022853. E-mail address: [email protected] (A. Shojaei). 0266-3538/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2007.03.009
During frictional braking, kinetic energy of a moving vehicle is primarily transformed to heat at the contact surface of friction pair, i.e., stator (friction material) and rotor (wheel or disc). The generated frictional heat is distributed between stator and rotor, raising the sliding surface temperature and inducing thermal distortions which may lead to thermal damages and hot spots [5–7]. Temperature rise of rotor is primarily dependent on its thermal conductivity and thermal interaction of friction pair [8,9]. Higher values of thermal conductivity and thermal diffusivity of rotor reduce its bulk and surface temperatures and lower the risk of thermal damage. Consequently, high thermal conductivity of rotor has been accepted as a major design criterion [10]. However, thermal interaction of friction pair is noticeably dominated by properties of both friction material and rotor. In the polymer-based composite friction materials, thermal interaction is affected by both mechanical properties
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and thermal characteristics of the friction materials [1,5]. For instance, a composite material with low elastic compression modulus creates a conformable surface and it in turn provides larger actual contact surface area, increasing the heat conduction from the friction material. The other important characteristic encouraging the heat conduction through friction material is thermal conductivity. Polymer-based composite friction materials have normally low thermal conductivity, namely less than 1 W/m C. However, any attempt to increase the thermal conductivity improves the ability of the friction material in transferring larger portion of the generated heat, leading to reduction of the contact surface temperature [9]. Moreover, our recent work indicated that increasing thermal conductivity of the composite friction material can also help to improve the process cycle and reduce the molding time significantly [11]. Published research activities concerning the thermally conductive composites show that the higher thermal conductivity can be achieved by the addition of thermally conductive fillers, particularly metals and metal alloys, to the polymer matrix. However, most of these studies have been limited to two-phase systems, including polymer matrix and thermally conductive filler. To predict the thermal conductivity, many attempts have been made to propose a suitable model relating the thermal conductivity of the polymer–filler system to thermal conductivities of individual components [12–17]. It has been observed that in addition to thermal conductivity of individual components, thermal conductivity of the composite is dependent on such factors as polymer–filler interaction and filler characteristics, namely type and shape of filler. Therefore, any successful conduction model should take into consideration these parameters as well. Owing to this, analysis of thermal conductivity of each polymer–filler system should be performed independently. This analysis for composite friction material becomes much more complicated due to the presence of different additives in the formulation. Application of a generation of composite friction material, which is known as semi-metallic, has been popular since the 1970s [2]. In these materials, metallic additives are primary constituents which may be various metals such as copper, steel, iron, brass and aluminum in the form of fibers or particles. Since the metallic additives improve the thermal behavior of the semi-metallic material, such a friction material is suitable for higher temperature applications and is primarily used for heavy duty operation [2]. The friction and wear of semi-metallic materials has been investigated extensively [18–21]. However, to the best knowledge of the authors, no effort has been made to precisely analyze the influences of individual parameters on the thermal characteristics, particularly thermal conductivity, of any kind of friction material such as semi-metallic ones. The present study is an attempt to investigate the parameters increasing the thermal conductivity of a conformable composite friction material which is used in the brake system of railroad vehicles [22,23]. Conformable fric-
tion materials have high compressibility in which compression modulus is less than 500 N/mm2 [1,5]. In this study, various friction materials are prepared by adding different thermally conductive particles into a commercially available friction material called here base material, such that its compressibility is retained. Thermal conductivity measurements are carried out for all obtained materials. The experimental results are also employed to develop a thermal conductivity model for the rubber-based composite friction materials used in this investigation. Additionally friction and wear characteristics of such thermally conductive friction materials are presented. 2. Thermal conductivity models of particle filled polymers Prediction of effective thermal conductivity of composite materials, particularly two-phase systems, has been the subject of many investigations for more than a century [24–30]. Maxwell [24] was the first to propose a theoretical model for a two-phase system including homogenous spherical inclusions distributed uniformly in a homogenous continuous medium or matrix as follows: k f þ 2k m þ 2/ðk f k m Þ kc ¼ km ð1Þ k f þ 2k m /ðk f k m Þ where kc, kf and km are the thermal conductivities of composite, filler and matrix, respectively, and / is the filler volume fraction. A review of other models for effective thermal conductivity of composite materials is presented by Progelhof et al. [26]. The values of thermal conductivity predicted by all of these models are bounded between parallel model
(kc = kf/ + km(1 /)) and series model k1c ¼ 1/ þ k/f . km The effective thermal conductivity of composites can also 1/ Þ. be calculated by the geometric mean model ðk c ¼ k /f k m In order to take into account the geometric parameters of fillers and filler–matrix interaction, available theoretical models must be modified appropriately. This may be done by including correction factors into the theoretical models, which are often obtained based on the experimental data and reflect the topology of the filler and polymer–filler interaction. For instance, Kusy and Corneliussen [12] proposed a semi-empirical model by including a correction factor into the parallel conduction model as follows: k c ¼ /k f þ ð1 /Þðkk m Þ ð2Þ where k is called a metallic conduction coefficient which is a measure of polymer–filler contact and filler topology and can be a function of matrix volume fraction. Another semi-empirical model to predict the effective thermal conductivity of filled thermoplastics has been proposed by Agari and Uno [27] as follows: log k c ¼ VC f log k f þ ð1 V Þ logðC m k m Þ ð3Þ where V is the volume content of fillers, Cm represents the effect of crystallinity of the thermoplastic and Cf is the coefficient of ease in forming conductive chains of fillers. The parameters Cm and Cf are extracted from experimental results for each polymer–filler system.
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For a two-phase system, Mamunya et al. [15] modified the geometric mean model as log k c ¼ log k m þ ðlog k f log k m Þð/=F Þ
N
ð4Þ
where F is the packing density coefficient representing geometrical characteristics of filler and N is a parameter which is obtained based on experimental results. Despite several models for two-phase systems, there are only a few publications concerning the thermal conductivity models for multi-component systems, for instance in [29,30]. An important model in this regard is the Agari’s model [30] which is the extension of their two-phase model, i.e., Eq. (3), to multi-component systems as follows: log k c ¼ V m logðC m k m Þ þ V 1 C f1 log k f1 þ V 2 C f2 log k f2 þ ð5Þ in which all the parameters have the same meaning as explained for Eq. (3). 3. Design criteria for preparation of friction materials with high thermal conductivity In this work, a commercially available composite friction material employed in the braking system of railroad vehicles is used as base material (BM). Table 1 presents the composition of this material. In Table 1, composition of the BM is presented by both PHR and weight fraction. Since the theories of effective thermal conductivity of composite are presented based on volume fraction of individual components, the composition is also given in terms of volume fraction calculated based on the weight fraction of individual components. 3.1. Selection of thermally conductive fillers Five different fillers are selected in this work based on their thermal conductivity, applicability in friction materials and cost. The selected materials are copper, aluminum, brass, aluminum oxide and talc. Thermophysical properties of the selected fillers, taken from literature, are presented in Table 2. Among the selected fillers, copper, aluminum and Table 1 Composition of base friction material (BM) Ingredients
PHRa
Weight fraction
Volume fraction
Unchangeable part SBR 1502 Phenolic resin Rubber curing agents Coal powder
100 25 17.75 82
0.23 0.057 0.041 0.19
0.424 0.0812 0.036 0.244
0.06 0.06 0.1 0.16 0.05 0.053
0.014 0.0137 0.069 0.068 0.018 0.032
Changeable part Steel wool Iron powder Calcium carbonate Barite Iron oxide (magnetite) Iron oxide (limonite) a
26 26 45 70 22 23
Part per hundreds of rubber by weight.
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Table 2 Thermophysical properties of selected thermally conductive fillers Thermal conductivity (W/m C)
Copper Brass (70 Cu, 30 Zn) Aluminum Aluminum oxide Talc
394 111
8940 8520
383 385
204 33*
2700 3400**
896 760***
10.7
Density (kg/m3)
Specific heat (J/kg C)
Fillers
2.78
820
Ref.
[31] [32]
[32] [30]*, [33]**, [32]*** [17,34]
brass have the highest values of thermal conductivity, while the other two fillers show relatively lower values of thermal conductivity. The main reason to select these latter fillers is due to their performance in friction and thermal conductivity of composite materials. For instance, it has been reported that talc is more effective than copper in increasing thermal conductivity of polypropylene composite due to better interconnectivity of the talc crystals [17]. Moreover, aluminum oxide may be used as an abrasive powder in the friction materials [35]. 3.2. Formulation of the friction materials To enhance the thermal conductivity of the BM, the selected fillers are included into the compound. However, as the purpose of the present work is to obtain the conformable friction material, both the compressibility and frictional properties of the BM should be retained after addition of the fillers. To achieve these requirements, two constraints is accounted for in designing new materials including (1) the volume fraction of rubber component in formulations should not be less than a minimum value, i.e., 0.4; and (2) the amount of coal powder in formulations should be retained, i.e., 82 PHR, compared to the BM. Experimental results show that the compressibility of the friction materials is strongly influenced by the rubber volume fraction at a specified content of rubber curing system and phenolic resin. For the BM, when the volume fraction of SBR is kept higher than 0.4, the compression modulus of the friction material falls below 500 N/mm2 which is low enough to obtain a conformable friction material [22,36]. On the other hand, as coal powder is a low price material which controls the frictional properties of the friction material, we also keep unchanged PHR of coal powder in all new formulations. To design formulation of new friction materials, the composition of the BM in terms of PHR is considered as base formulation and then it is divided to two parts: (1) unchangeable part, which includes the rubber and its curing agents, phenolic resin and coal powder and (2) changeable part containing rest of components which are mainly the fillers. Table 1 illustrates these two parts of the compound. To satisfy the mentioned constraints, the new for-
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Table 3 The methodology used for preparing formulation of different friction materials containing copper in terms of PHR Ingredients
C-Cu-10
C-Cu-20
C-Cu-30
C-Cu-40
C-Cu-48
C-Cu-57
SBR 1502 Phenolic resin Rubber curing agents Coal powder
100 25 17.75 82
100 25 17.75 82
100 25 17.75 82
100 25 17.75 82
100 25 17.75 82
100 25 17.75 82
Calcium carbonate Iron powder Steel wool Barite Iron oxide (Limonite) Iron oxide (magnetite) Cu
1.3 26 26 70 23 22 43.7
0 0 9.5 70 23 22 87.5
0 0 0 36 23 22 131
0 0 0 0 15 22 175
0 0 0 0 0 0 212
0 0 0 0 0 0 300
Table 4 Formulation of different friction materials containing copper in terms of volume fraction Ingredients
C-Cu-10
C-Cu-20
C-Cu-30
C-Cu-40
C-Cu-48
C-Cu-57
SBR 1502 Phenolic resin Rubber curing agents Coal powder
0.445 0.085 0.038 0.256
0.447 0.086 0.038 0.257
0.456 0.087 0.039 0.262
0.469 0.089 0.04 0.027
0.48 0.092 0.041 0.276
0.459 0.088 0.039 0.263
Calcium carbonate Iron powder Steel wool Barite Iron oxide (limonite) Iron oxide (magnetite) Cu
0.002 0.014 0.015 0.071 0.033 0.019 0.021
0 0 0.005 0.071 0.034 0.019 0.043
0 0 0 0.037 0.034 0.019 0.065
0 0 0 0 0.023 0.02 0.09
0 0 0 0 0 0 0.111
0 0 0 0 0 0 0.15
mulations are obtained by replacing the fillers from changeable part of the base formulation with thermally conductive fillers. In order to reveal the effect of filler type on thermal conductivity of the friction material, only one thermally conductive filler is included in each formulation. However, to investigate the role of filler content on the thermal conductivity, different compounds with different contents of given filler are prepared. Table 3 presents the formulation of different friction materials containing various contents of copper and the methodology used to replace the fillers of BM with conductive fillers. In Table 3, each formulation containing copper is designated by C-Cu followed by two digits indicating the weight percent of copper. The same methodology is used for providing friction materials containing other conductive fillers. Table 4 gives formulations of Table 3 in terms of volume fraction calculated based on weight fractions. As seen, the volume fraction of rubber is higher than the limit value for all friction materials containing copper. Owing to different densities of conductive fillers, application of mentioned methodology for other fillers may be resulted in some friction materials with rubber content less than the limit value. 4. Experimental 4.1. Materials and preparation of specimens The ingredients of the base friction material indicated in Table 1 involve (1) polymers which are styrene butadiene
rubber (SBR 1502) from BIPC Co. (Iran) as polymer matrix and phenolic resin (Novolac IP 502) from Rezitan Co. (Iran); (2) curing agents of SBR including MBTS, zinc oxide, stearic acid and sulfur; and (3) fillers comprising coal powder, iron powder, steel wool, calcium carbonate, barite (barium sulfate), iron oxide (both magnetite and limonite). The physical properties of materials utilized in the BM are reported in Table 5. Copper powder, aluminum chips, brass chips, aluminum oxide and talc are used as thermally conductive fillers. All of the fillers employed in this investigation are supplied from local companies and are industrial grade. Table 6 illustrates the shape and particle size of these fillers. Two different sizes of brass chips are used to investigate the particle size effect. The specimens are prepared by mixing ingredients of each formulation using a two roll mill and then cured by a hot press at 150 C for 20 min. The cured specimens are then post cured at 180 C for 12 h and finally they are cut in desired dimensions. 4.2. Measurements 4.2.1. Thermal conductivity Thermal conductivity measurements are carried out under steady state condition, by utilizing the thermal conductance tester model TCM-1 (Mehr-Sanat Pajooh, Iran), which is based on the comparison method with small size specimen as explained in ASTM E1530. Disc shaped specimens with diameter of 50 mm and thickness of 10 mm are
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Table 5 Properties of ingredients used in the BM Fillers
Thermal conductivity (W/m C)
Density (kg/m3)
Comments
SBR 1502 Phenolic resin Coal powder Calcium carbonate Iron powder Steel wool Barite Iron oxide (limonite) Iron oxide (magnetite)
0.19–0.25 0.15 0.26 3 73.7 25 1.72* 5.1* 5.1
980 1280 1400 2700 7870 7750 4300** 3000** 5100
Bold faced value is used in calculations. Pure gum vulcanizate [37] Average value of casting resin [38] Ref. [39] Ref. [33] Ref. [31] Stainless steel 410 [40] Refs. [17,34]*; ** measured value *To be considered same as magnetite; **measured value Refs. [17,34]
Fillers
Particle size (lm)
Particle shape
Copper Brass chips I Brass chips II Aluminum chips Aluminum oxide powder Talc powder
30–65 (measured) 30–100 (measured) 100–450 (measured) 50–300 (measured) Very fine [17,34]
Spherical Platelet Platelet Platelet Platelet
Very fine (13–105 nm) [33]
Spherical or irregular
used in the instrument for thermal conductivity measurements. A known constant heat flux is applied from one side of the specimen. When the thermal equilibrium is attained and the system approaches to steady state situation, the temperature drop (DT) is recorded by K type thermocouples installed on top and bottom of the specimen. Knowing the values of heat flux, measured by heat flux transducer (HFT), temperature drop and thickness, the thermal conductivity can be determined by employing one-dimensional Fourier’s law of conduction. However, before performing the experiments for unknown specimens, HFT needs to be calibrated using two standard specimens with known thermal conductivities. The standard specimens used in this study are: Pyrex glass and stainless steel 304. All measurements are carried out approximately in the similar temperature range, i.e., 25–70 C. 4.2.2. Density The density of friction materials is determined according to procedure proposed in ASTM D792, which is based on Archimedes’ principle. 4.2.3. Optical microscopy In order to investigate the distribution of thermally conductive fillers in the composites and determine the particle size, an optical microscope model PME3 Olympus equipped to image analyzer software Omnimet Advantage (Buehler) is used.
against gray cast iron counter ring whose inner diameter is 300 mm. Friction tests are carried out under constant sliding speed of 700 rpm and braking pressure of 200 psi. After completion of the friction tests, the samples are weighed once again, and the cumulative weight loss is reported as specific wear in terms of volume. 4.2.5. Compressibility The elastic compression modulus of the friction materials as a measure of compressibility of the friction materials is measured using Rockwell hardness tester in accordance with methodology presented in UIC Code [41]. Details are given in [5]. 5. Results and discussion of the experimental data 5.1. Thermal conduction characteristics Fig. 1 shows variations of thermal conductivity of composite friction materials with volume fraction of conductive fillers. As shown in Fig. 1, in all cases, the thermal conduc-
7 BM Cu
6
Al Brass I Brass II
5
Al2O3 Talc
k (w/m.K)
Table 6 Particle size of the thermally conductive fillers
4
3 2 1 0
4.2.4. Frictional properties The friction tests are carried out on a small scale padon-ring type friction tester. Composite specimens with size of 27 mm · 25 mm · 5 mm are hydraulically pressed
0
0.05 0.1 0.15 0.2 0.25 Volume fraction of conductive filler
0.3
Fig. 1. Thermal conductivity of composite friction materials contained various thermally conductive fillers.
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tivity increases uniformly by increasing volume fraction of the conductive fillers. The results also show that thermal conductivity of the composite friction materials filled with thermally conductive fillers lies between 0.48 and 5.8 W/ m K, approximately up to 12 times increase in the effective thermal conductivity, depending on the type and content of the filler. Furthermore, the measured thermal conductivities are consistent with findings of other researchers [12,16,17]. From Fig. 1, it is found that the compound C-Al-40 containing aluminum chips shows the maximum thermal conductivity among all compounds (kC-Al-40 = 5.8 W/m C). This can be explained by relatively high thermal conductivity of aluminum (kAl = 204 W/m C) and its high volume fraction (which is around 25 vol%) due to its low density compared with copper which is 15% by volume in C-Cu-57. However, as shown in Fig. 1, at the same volume fraction, the thermal conductivity of copper filled friction material is slightly higher than the thermal conductivity of aluminum filled material. This behavior of thermal conductivity might be expected, because the thermal conductivity of copper is approximately twice the thermal conductivity of aluminum. As can be realized from Table 2, thermal conductivity of the selected conductive fillers is in the order as Cu > Al > brass > Al2O3 > talc. However as shown in Fig. 1, at the
same volume fraction, compounds filled with these fillers show different sequences as C-BrII > C-BrI C-Cu > C-Al > C-talc > C-AlO. This discrepancy in the thermal conductivity of the compounds can not be explained solely by the differences in the thermal conductivity of the fillers, but other parameters such as geometry of the filler and microstructure of the composite should be taken into consideration. As can be seen in Fig. 1, thermal conductivity of compounds filled with large size of brass chips (brass II in Table 6) is higher than the thermal conductivity of brass chips having small size (brass I in Table 6) at the same volume fraction. Furthermore, although the thermal conductivity of copper is approximately four times higher than the thermal conductivity of brass, the brass filled compounds show higher thermal conductivities than friction materials contained copper at the identical volume fraction. As the densities and specific heat capacities of these two fillers are approximately equal (see Table 2), this behavior can be attributed to the geometry of the fillers and microstructure of the composite. The particle size of the brass chips is larger than the copper (see Table 6). In addition, brass chips have platelet shape; while the copper particles are approximately spherical (see Fig. 2). In the platelet shaped fillers, the chance of creating partial interconnectivity among some particles increases, leading to higher thermal conduc-
Fig. 2. Optical micrograph of friction materials filled with thermally conductive fillers: (a) copper, (b) aluminum chips, (c) brass chips I and (d) brass chips II.
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tivity of the composite [17]. On the other hand, as observed in brass chips filled compounds, thermal conductivity increases by increasing the size of platelet shaped fillers. These results emphasize that both shape and size of fillers have important role on thermal conductivity. Lower value of thermal conductivity of aluminum filled compounds with respect to compounds containing brass chips may be related to smaller size of aluminum chips (compared to brass II). In addition, other thermophysical properties of these fillers, i.e., density and specific heat capacity are different which may be regarded as source of the discrepancy observed in the thermal conductivity of the composite. Experimental data obtained in this study indicates that the fillers with larger size and platelet shape are more effective than the fillers with smaller size and spherical shape in enhancing the effective thermal conductivity of the friction material. Both talc and aluminum oxide are very fine particles and have the moderate thermal conductivities. Therefore, as shown in Fig. 1, compounds filled with these two fillers have the lower thermal conductivities among all compounds. However, despite lower thermal conductivity of talc with respect to aluminum oxide, talc filled compounds show relatively higher thermal conductivity. As reported by Weidenfeller et al. [17], platelet shape of talc may help to creating interconnectivity among the particles and this may be regarded as major source of higher thermal conductivity of talc filled compounds. 5.2. Physical and frictional characteristics Fig. 3 illustrates variations of measured density of friction materials with volume fraction of thermally conductive fillers used in this investigation. As seen in the figure, density of compound increases by increasing content of copper and brass from 1730 up to 2300 kg/m3. However,
Density (Kg/m^3)
2300 2200
BM Cu
2100
Al Brass I
2000
Brass II Al2O3
1900
Talc
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Table 7 Frictional properties and compressibility of thermally conductive friction materials Friction material
Coefficient of friction
Specific wear (cm3)
Elastic compression modulus (N/mm2)
Volume fraction of SBR in the compound
BM C-Cu-48 C-BrII-48 C-Al-48 C-talc-48 C-AlO-48
0.57 0.5 0.48 0.42 0.22 0.6
0.17 0.18 0.18 0.27 0.08 1
410 380 440 800 920 580
0.42 0.48 0.477 0.38 0.385 0.406
for aluminum, aluminum oxide and talc, the inverse behavior is observed, i.e., density of friction material decreases by increasing content of these fillers. This behavior can be clearly interpreted by the density of the filler. Low density fillers lead to low density composites and vice a versa. The friction, wear and compressibility of the friction materials are presented in Table 7. It is found that the specific wear and COF of the friction materials strongly depend on the conductive fillers used in the formulation. As the polymer matrix of all compounds is the same, therefore the observed difference in specific wear of different materials could be attributed to filler dependent mechanisms such as abrasive and adhesive mechanisms [42]. The highest changes in COF and specific wear with respect to BM belong to the aluminum oxide and talc filled compounds. However, experimental results presented here indicate that among all thermally conductive fillers copper powder shows relatively high and stable COF as well as low wear. Such frictional behavior has been reported for copper fiber filled phenolic resin based friction material [43]. Therefore, this filler seems to have a great potential to be used for producing thermally conductive railroad rubber-based friction materials. The compressibility of the friction materials depends on the rubber content. From Table 7, it is seen that the friction materials C-Al-48 and C-talc-48 have the higher compression modulus which have the lowest content of rubber. Of course, the filler can have a slight effect on compressibility. For instance, lower value of modulus for C-Al-48 with respect to C-talc-48 can be due to the fact that the aluminum is softer than talc. 6. Semi-empirical thermal conductivity model
1800
6.1. Development of the model 1700 1600 1500 0
0.05 0.1 0.15 0.2 0.25 Volume fraction of conductive filler
0.3
Fig. 3. Density of composite friction materials contained various thermally conductive fillers.
The geometric mean model for multiphase systems can be given as n Y / k c ¼ k /mm k /1 1 k /2 2 . . . k /n n ¼ k /mm ki i ð6Þ i¼1
where m indicates the continuous phase or matrix, n is the total number of dispersed phase or additives, ki and /i rep-
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resent the thermal conductivity and volume fraction of ith component, respectively, so that /m + /1 + /2 + + /N = 1. Based on Eq. (6), one can calculate the effective thermal conductivity of the composite if volume fraction and thermal conductivity of each component are known. As an example, the measured thermal conductivities of copper filled friction materials and the calculated ones based on Eq. (6) are illustrated in Fig. 4. From the figure, one can find that the model prediction and experimental data for the BM is in good agreement. However, by addition of copper, the measured values are deviated from the model prediction, and the deviation increases by increasing the copper content. More or less, similar results were also observed for other thermally conductive fillers used in this study. To predict the thermal conductivity of the composite accurately, Eq. (6) needs to be modified appropriately. To do this, for each dispersed phase distributed within a specific matrix, a corrected thermal conductivity is introduced as follows: ~k i ¼ F i ð/i Þk i ð7Þ where ~k i and ki are the corrected and real thermal conductivities of ith dispersed phase, respectively, and Fi(/i) is referred to filler correction coefficient which is generally function of volume fraction of the dispersed phase. Function Fi for an additive in a matrix can be a measure of indirect effects on thermal conductivity such as shape and size of filler as well as matrix–filler interaction. Such a correction coefficient in thermal conduction models has been proposed by many researchers [12,15,27]. Replacing the real thermal conductivities of dispersed phases with corrected thermal conductivities in Eq. (7), and rearranging the resultant equation leads to the following expression:
5 Calculated by Geometric mean model
k (w/m.K)
4
Experimental results
3
/
/2
/
k c ¼ F 1 ð/1 Þ 1 F 2 ð/2 Þ . . . F n ð/n Þ n k /mm
n Y
/
ki i
ð8Þ
i¼1
Eq. (8) may be expressed in a simple form as k c ¼ Að/1 ; /2 ; . . . ; /n Þk /mm
n Y
/
ki i
ð9Þ
i¼1
in which A is called overall correction function of conduction which is generally a function of volume fraction of the additives and might be determined from experimental results. 6.2. Application of the proposed model for composite friction materials It is somewhat difficult to obtain the function A based on Eq. (9) in the present form. For composite friction material studied in this work, one can make the following assumptions to simplify the proposed model: (1) The SBR rubber along with its curing system is considered as matrix, and other components are accounted for dispersed phases. (2) As was observed in preceding section, selected thermally conductive fillers have significant effects on thermal conductivity of the friction material, and alter considerably the thermal conductivity of the composite by alteration of their volume fraction. In addition, the presence of these fillers causes a strong deviation from the theoretical geometric mean model. Therefore, all fillers in the compound are divided to two groups, including thermally conductive fillers and non-conductive fillers. The non-conductive fillers in the BM do not deviate the thermal conductivity of the composite with respect to theoretical value. This can be found from the result presented in Fig. 4. According to this issue, we assume that the overall correction function of conduction is function of volume fraction of conductive fillers. Of course, it should be noted that correction coefficient of all non-conductive fillers appears as a mean constant value in function A and it is close to 1. According to assumptions presented above, and as only one conductive filler has been included in the materials, proposed model, i.e., Eq. (9), is simplified for friction materials as
2
1
k c ¼ Að/t Þk /mm k /t t
N Y
/
ki i
ð10Þ
i¼1
0 0
0.1 Volume fraction of Cu
0.2
Fig. 4. Comparison of calculated effective thermal conductivity of composite using geometric mean model and experimental data at different volume fractions of copper.
where subscript t represents the thermally conductive filler and N shows the total number of non-conductive fillers. According to simplified form of present model, i.e., Eq. (10), function A can be obtained based on experimental results presented in Section 5 as follows:
A. Shojaei et al. / Composites Science and Technology 67 (2007) 2665–2674 Table 8 Function A for compounds filled with thermally conductive fillers
Table 9 Formulation of different compounds containing combination of thermally conductive fillers in terms of volume fraction
Compound
Function A
C-Cu C-Al C-brass I C-brass II C-AlO C-talc
802.5/3 33.2/2 + 58.4/ + 1.125 55.9/3 32.7/2 + 8.1/ + 3.26 813.2/3 + 185.4/2 + 43/ + 1.9 1208/3 + 2772/2 + 246/ 0.939 6.4/2 + 3.1/ + 1.95 3.3/2 + 2.5/ + 2.65
Að/t Þ ¼
k ec /t Qn
k /mm k t
where k ec is the experimental thermal conductivity of friction materials. Using Eq. (11), value of A can be determined at each volume fraction of known conductive filler, from which one can express a functional form for A. According to this procedure, a series of polynomial functions is obtained for conductive fillers by using regression analysis and the results are presented in Table 8. 6.3. Development of the model for friction material containing more than one thermally conductive filler Eq. (10) can be applicable for friction material with one conductive filler. If more than one conductive filler is included in the friction material, according to assumption 2 mentioned above, Eq. (10) should be expressed as ! ! M N Y Y / / j k c ¼ Að/t1 ; /t2 ; . . . ; /tM Þk /mm k tj ki i ð12Þ j¼1
C-Cu/ Al-1
C-Cu/ Al-2
C-Cu/BrI/ Al-1
C-Cu/BrI/ Al-2
SBR 1502 Phenolic resin Rubber curing agents Coal powder Cu Aluminum chips Brass chips I
0.43 0.083 0.037
0.45 0.086 0.038
0.45 0.086 0.039
0.44 0.084 0.038
0.26 0.095 0.094 0
0.27 0.098 0.065 0
0.26 0.05 0.065 0.052
0.25 0.077 0.063 0.063
u
Að/t1 ; /t2 ; . . . ; /tM Þ ¼ Að/t1 Þ t1 Að/t2 Þ Að/tM Þ
Table 10 Comparison of measured and calculated thermal conductivities for different compounds filled with combination of thermally conductive fillers Compound
kmeasured (W/m K)
kcalculated (W/m K)
C-Cu/Al-1 C-Cu/Al-2 C-Cu/BrI/Al-1 C-Cu/BrI/Al-2
4 3.3 2.6 3.6
4.2 3.7 2.9 3.9
are presented in Table 9. The comparison between measured value and calculated one based on Eqs. (12) and (13) for each compound is given in Table 10. As can be seen, good agreement is observed in all cases, indicating the applicability of the proposed model to predict the thermal conductivity of the friction material. 7. Conclusions
i¼1
where M is the total number of thermally conductive fillers in the friction material. Determination of function A for such multi-conductive filler composite based on procedure mentioned for friction material containing one conductive filler is mathematically tedious and experimentally costly and time consuming. In such systems, we suggest the following model for function A as M Y
Ingredients
ð11Þ
/i i¼1 k i
¼
2673
ut M
ut
2
. . . Að/tM Þ
utM
ð13Þ
j¼1
where Að/tj Þ is overall correction function of conduction for a conductive filler as reported in Table 9, utj is the ratio of volume of jth conductive filler to total volume of conductive fillers in the friction material such that ut1 þ ut2 þ þ utM ¼ 1: Indeed, Eq. (13) is a geometric mean model based on A function of each filler and total volume of conductive fillers and it is called mean overall correction function of conduction. To verify the validity and applicability of the proposed model, some friction materials containing several conductive fillers are prepared and then their thermal conductivities are measured. The compositions of these compounds
Thermal conductivity of a rubber-based composite friction material has been studied in this investigation. Various thermally conductive fillers including copper, brass chips with two sizes, aluminum chips, aluminum oxide and talc have been selected and the effect of addition of these fillers on the thermal conductivity of the base friction material has been examined. It is found that the thermal conductivity of the friction material increases continuously by increasing the content of the selected fillers. Maximum thermal conductivity is related to aluminum chips filled compound due to higher volume fraction of this filler. However, at a given volume fraction, friction material containing larger size of brass chips shows higher thermal conductivity, which is a consequence of the shape and size of the fillers. Based on geometric mean model, a semi-empirical model of thermal conductivity is proposed for multiphase systems. In this model, the fillers are categorized into thermally conductive and non-conductive. To take into account the indirect effects of fillers on the effective thermal conductivity of composite, function A called overall correction function of thermal conduction is introduced for a system containing multi-non-conductive fillers and only one conductive filler. In addition, the model is extended to systems containing multi-conductive and non-conductive fillers, in which the
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correction function for such a system can be calculated based on function A of each thermally conductive filler obtained independently. Acknowledgements Authors are grateful to Mashin Lent Tehran Company, particularly Mr. Alaei who is general director of the company, to provide the materials and compounding machines used in this work. All the thermal conductivity measurements were carried out in Iran railway research center. The authors would like to express special thanks for their support. References [1] Gibson PA. Composition friction materials for the replacement of cast iron railway blocks. IMechE seminar publication on railway traction and braking; 1996. p. 75–85. [2] Jacko MG, Rhee SK. Brake linings and clutch facings. In: KirkOthmer (Ed.), Encyclopedia of chemical technology; 1987 [chapter 4]. [3] Takashi, Osamu N. Friction materials. US Patent 5576369; 1996. [4] Griffith AM. Composition railroad friction material with synthetic fiber content. US Patent 4217255; 1980. [5] Abbasi F, Shojaei A, Katbab A. Thermal interaction between polymer-based composite friction materials and counterfaces. J Appl Polym Sci 2001;81:364–9. [6] Panier S, Dufre´noy P, Weichert D. An experimental investigation of hot spots in railway disc brakes. Wear 2004;256:764–73. [7] Anderson AE, Knapp RA. Hot spotting in automotive friction systems. Wear 1990;135:319–37. [8] Dunaevsky VV. Prediction of railroad friction braking temperatures: prediction of average bulk and average surface temperatures of railroad wheels and brake discs. Tribol Trans 1991;34(3):343–52. [9] Limpert R. Brake design and safety. USA: SAE Publication Group; 1992. [10] Bijwe J. Composites as friction materials: recent developments in nonasbestos fiber reinforced friction materials – a review. Polym Comp 1997;18(3):378–96. [11] Shojaei A. A numerical investigation on the cure characteristics of railroad composite brake blocks during the compression molding process. Int Polym Process 2006;XXI:421–31. [12] Kusy RP, Corneliussen RD. The thermal conductivity of nickel and copper dispersed in poly vinyl chloride. Polym Eng Sci 1975;15(2):107–12. [13] Lu X, Xu G. Thermally conductive polymer composites for electronic packaging. J Appl Polym Sci 1997;65:2733–8. [14] Yu S, Hing P, Hu X. Thermal conductivity of polystyrene-aluminum nitride composite. Composites A 2002;33:289–92. [15] Mamunya YP, Davydenko VV, Pissis P, Lebedev EV. Electrical and thermal conductivity of polymers filled with metal powders. Eur Polym J 2002;38:1887–97. [16] Kumlutas D, Tavman IH, Coban MT. Thermal conductivity of particle filled polyethylene composite materials. Comp Sci Tech 2003;63:113–7. [17] Weidenfeller B, Hofer M, Schilling FR. Thermal conductivity, thermal diffusivity and specific heat capacity of particle filled polypropylene. Composites A 2004;35:423–9.
[18] Rhee SK. Wear of metal-reinforced phenolic resins. Wear 1971;18:471–7. [19] Libsch TA, Rhee SK. Microstructural changes in semimetallic disc brake pads created by low temperature dynamometer testing. Wear 1978;46:203–12. [20] Liu T, Rhee SK. High temperature wear of semimetallic disc brake pads. Wear 1978;46:213–8. [21] Anderson AE. Friction and wear of automotive brakes. In: Henry SD, editor. Metal handbook, vol. 18. New York: ASM International; 1992. p. 569–77. [22] Haddadi E, Abbasi F, Shojaei A. Wear and thermal effects in low modulus polymer-based composite friction materials. J Appl Polym Sci 2005;95:1181–9. [23] Shojaei A, Abbasi F. Cure kinetics of a polymer-based composite friction material. J Appl Polym Sci 2006;100:9–17. [24] Maxwell JC. A treatise on electricity and magnetism. 3rd ed. Oxford: Clarendon Press; 1881. [25] Bruggeman D. Dielectric constant and conductivity of mixtures of isotope materials. Ann Phys 1935;24:636. [26] Progelhof RC, Throne JL, Ruetsch RR. Methods for predicting the thermal conductivity of composite systems: a review. Polym Eng Sci 1976;16(9):615–25. [27] Agari Y, Uno T. Estimation on thermal conductivities of filled polymers. J Appl Polym Sci 1986;32:5705–12. [28] Lewis T, Nielsen L. Dynamic mechanical properties of particulatefilled polymers. J Appl Polym Sci 1970;14:1449. [29] Budiansky B. Thermal and thermoelectric properties of isotropic composite. J Comp Mater 1970;4:286. [30] Agari Y, Tanaka M, Nagai S. Thermal conductivity of a polymer composite filled with mixture of particles. J Appl Polym Sci 1987;34:1429–37. [31] Kotzin EL. Metal caster’s reference and guide. USA: American Founderymer Society; 1972. [32] Holman JP. Heat transfer. 8th ed. New York: McGraw-Hill; 1997. [33] Wypych G. Handbook of fillers. 2nd ed. ChemTec Publishing; 1999. [34] Clauser C, Huenges E. Thermal conductivity of rocks and minerals. In: Ahrens TJ, editor. Rock physics and phase relations. American Geophysical Union Referencel; 1995. [35] Lu Y, Wright MA. Optimizing friction formulation technique with emphasis on relational grade analysis. In: 45th International SAMPE symposium, May 21–25, 2000. p. 1972–78. [36] Fahimian M. Study of parameters affecting thermal conductivity of the composite friction materials. MSc thesis in Farsi, Department of Chemical and Petroleum Engineering, Sharif University of Technology; 2005. [37] Brandrup PJ, Immergut EH, Grulke EA. Polymer handbook. 4th ed. New York: John Wiley; 1999. [38] Harper CA. Handbook of plastics, elastomers and composites. 3rd ed. New York: McGraw-Hill; 1996. [39] Cardelli F. Materials handbook. New York: Springer; 2000. [40] Booser ER. Tribology data handbook. Boca Raton: CRC Press; 1997. [41] UIC Code 541-4 OR. Brakes with composition brake blocks. 2nd ed. 1990. [42] Jacko MG, Tsang PHS, Rhee SK. Automotive friction materials evolution during the past decade. Wear 1984;100:503–15. [43] Ho SC, Lin JHC, Ju CP. Effect of fiber addition on mechanical and tribological properties of a copper/phenolic-based friction material. Wear 2005;258:861–9.
Thermally conductive rubber-based composite friction materials for railroad brakes – Thermal conduction characteristics A. Shojaei *, M. Fahimian, B. Derakhshandeh Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran 11365-9465, Iran Received 23 November 2005; received in revised form 13 February 2007; accepted 8 March 2007 Available online 20 March 2007
Abstract This study deals with the thermal conductivity of rubber-based composite friction materials used in railroad vehicles. Based on a commercially available railroad friction material, called here base material (BM), various friction materials containing different thermally conductive fillers (Cu, brass, Al, Al2O3 and talc) are fabricated and then their thermal conductivities are measured at various contents of the fillers. Addition of the thermally conductive fillers causes an increase in thermal conductivity of the friction material from 0.48 up to 5.8 W/m K, depending on the type and content of the filler. In addition, the experimental results reveal that the thermal conductivity of the friction material can be influenced by indirect effects including mainly the shape and size of the filler. Fillers with larger size and platelet shape are more effective in enhancing the thermal conductivity of the friction material. In order to provide an engineering tool to estimate the thermal conductivity of the friction materials, a new semi-empirical model is proposed for multiphase systems based on geometric mean model. In this model, the filler may be regarded thermally conductive or non-conductive. The model is first developed for friction material containing multi-non-conductive fillers and one thermally conductive filler and then is extended to a system containing multi-conductive and non-conductive fillers. The agreement between model predictions and experimental measurements is satisfactory. 2007 Elsevier Ltd. All rights reserved. Keywords: A. Polymer–matrix composites (PMCs); B. Friction; B. Thermal property; B. Thermally conductive fillers
1. Introduction Polymer-based composite friction materials are widely used in frictional brake systems of many vehicles, particularly in brake systems of railroad vehicles due to numerous advantages of this kind of materials such as good braking performance, long life, low braking noise and light weight [1]. Friction, wear and physical properties of such friction materials are governed by different ingredients in formulation of the composite (typically up to 20 different ingredients). Generally speaking, these ingredients can be categorized into primary groups based on their expected functions including binder or polymer matrix, friction modifiers, reinforcements and fillers [2–4]. *
Corresponding author. Tel./fax: +98 21 66164586; fax: +98 21 66022853. E-mail address: [email protected] (A. Shojaei). 0266-3538/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2007.03.009
During frictional braking, kinetic energy of a moving vehicle is primarily transformed to heat at the contact surface of friction pair, i.e., stator (friction material) and rotor (wheel or disc). The generated frictional heat is distributed between stator and rotor, raising the sliding surface temperature and inducing thermal distortions which may lead to thermal damages and hot spots [5–7]. Temperature rise of rotor is primarily dependent on its thermal conductivity and thermal interaction of friction pair [8,9]. Higher values of thermal conductivity and thermal diffusivity of rotor reduce its bulk and surface temperatures and lower the risk of thermal damage. Consequently, high thermal conductivity of rotor has been accepted as a major design criterion [10]. However, thermal interaction of friction pair is noticeably dominated by properties of both friction material and rotor. In the polymer-based composite friction materials, thermal interaction is affected by both mechanical properties
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and thermal characteristics of the friction materials [1,5]. For instance, a composite material with low elastic compression modulus creates a conformable surface and it in turn provides larger actual contact surface area, increasing the heat conduction from the friction material. The other important characteristic encouraging the heat conduction through friction material is thermal conductivity. Polymer-based composite friction materials have normally low thermal conductivity, namely less than 1 W/m C. However, any attempt to increase the thermal conductivity improves the ability of the friction material in transferring larger portion of the generated heat, leading to reduction of the contact surface temperature [9]. Moreover, our recent work indicated that increasing thermal conductivity of the composite friction material can also help to improve the process cycle and reduce the molding time significantly [11]. Published research activities concerning the thermally conductive composites show that the higher thermal conductivity can be achieved by the addition of thermally conductive fillers, particularly metals and metal alloys, to the polymer matrix. However, most of these studies have been limited to two-phase systems, including polymer matrix and thermally conductive filler. To predict the thermal conductivity, many attempts have been made to propose a suitable model relating the thermal conductivity of the polymer–filler system to thermal conductivities of individual components [12–17]. It has been observed that in addition to thermal conductivity of individual components, thermal conductivity of the composite is dependent on such factors as polymer–filler interaction and filler characteristics, namely type and shape of filler. Therefore, any successful conduction model should take into consideration these parameters as well. Owing to this, analysis of thermal conductivity of each polymer–filler system should be performed independently. This analysis for composite friction material becomes much more complicated due to the presence of different additives in the formulation. Application of a generation of composite friction material, which is known as semi-metallic, has been popular since the 1970s [2]. In these materials, metallic additives are primary constituents which may be various metals such as copper, steel, iron, brass and aluminum in the form of fibers or particles. Since the metallic additives improve the thermal behavior of the semi-metallic material, such a friction material is suitable for higher temperature applications and is primarily used for heavy duty operation [2]. The friction and wear of semi-metallic materials has been investigated extensively [18–21]. However, to the best knowledge of the authors, no effort has been made to precisely analyze the influences of individual parameters on the thermal characteristics, particularly thermal conductivity, of any kind of friction material such as semi-metallic ones. The present study is an attempt to investigate the parameters increasing the thermal conductivity of a conformable composite friction material which is used in the brake system of railroad vehicles [22,23]. Conformable fric-
tion materials have high compressibility in which compression modulus is less than 500 N/mm2 [1,5]. In this study, various friction materials are prepared by adding different thermally conductive particles into a commercially available friction material called here base material, such that its compressibility is retained. Thermal conductivity measurements are carried out for all obtained materials. The experimental results are also employed to develop a thermal conductivity model for the rubber-based composite friction materials used in this investigation. Additionally friction and wear characteristics of such thermally conductive friction materials are presented. 2. Thermal conductivity models of particle filled polymers Prediction of effective thermal conductivity of composite materials, particularly two-phase systems, has been the subject of many investigations for more than a century [24–30]. Maxwell [24] was the first to propose a theoretical model for a two-phase system including homogenous spherical inclusions distributed uniformly in a homogenous continuous medium or matrix as follows: k f þ 2k m þ 2/ðk f k m Þ kc ¼ km ð1Þ k f þ 2k m /ðk f k m Þ where kc, kf and km are the thermal conductivities of composite, filler and matrix, respectively, and / is the filler volume fraction. A review of other models for effective thermal conductivity of composite materials is presented by Progelhof et al. [26]. The values of thermal conductivity predicted by all of these models are bounded between parallel model
(kc = kf/ + km(1 /)) and series model k1c ¼ 1/ þ k/f . km The effective thermal conductivity of composites can also 1/ Þ. be calculated by the geometric mean model ðk c ¼ k /f k m In order to take into account the geometric parameters of fillers and filler–matrix interaction, available theoretical models must be modified appropriately. This may be done by including correction factors into the theoretical models, which are often obtained based on the experimental data and reflect the topology of the filler and polymer–filler interaction. For instance, Kusy and Corneliussen [12] proposed a semi-empirical model by including a correction factor into the parallel conduction model as follows: k c ¼ /k f þ ð1 /Þðkk m Þ ð2Þ where k is called a metallic conduction coefficient which is a measure of polymer–filler contact and filler topology and can be a function of matrix volume fraction. Another semi-empirical model to predict the effective thermal conductivity of filled thermoplastics has been proposed by Agari and Uno [27] as follows: log k c ¼ VC f log k f þ ð1 V Þ logðC m k m Þ ð3Þ where V is the volume content of fillers, Cm represents the effect of crystallinity of the thermoplastic and Cf is the coefficient of ease in forming conductive chains of fillers. The parameters Cm and Cf are extracted from experimental results for each polymer–filler system.
A. Shojaei et al. / Composites Science and Technology 67 (2007) 2665–2674
For a two-phase system, Mamunya et al. [15] modified the geometric mean model as log k c ¼ log k m þ ðlog k f log k m Þð/=F Þ
N
ð4Þ
where F is the packing density coefficient representing geometrical characteristics of filler and N is a parameter which is obtained based on experimental results. Despite several models for two-phase systems, there are only a few publications concerning the thermal conductivity models for multi-component systems, for instance in [29,30]. An important model in this regard is the Agari’s model [30] which is the extension of their two-phase model, i.e., Eq. (3), to multi-component systems as follows: log k c ¼ V m logðC m k m Þ þ V 1 C f1 log k f1 þ V 2 C f2 log k f2 þ ð5Þ in which all the parameters have the same meaning as explained for Eq. (3). 3. Design criteria for preparation of friction materials with high thermal conductivity In this work, a commercially available composite friction material employed in the braking system of railroad vehicles is used as base material (BM). Table 1 presents the composition of this material. In Table 1, composition of the BM is presented by both PHR and weight fraction. Since the theories of effective thermal conductivity of composite are presented based on volume fraction of individual components, the composition is also given in terms of volume fraction calculated based on the weight fraction of individual components. 3.1. Selection of thermally conductive fillers Five different fillers are selected in this work based on their thermal conductivity, applicability in friction materials and cost. The selected materials are copper, aluminum, brass, aluminum oxide and talc. Thermophysical properties of the selected fillers, taken from literature, are presented in Table 2. Among the selected fillers, copper, aluminum and Table 1 Composition of base friction material (BM) Ingredients
PHRa
Weight fraction
Volume fraction
Unchangeable part SBR 1502 Phenolic resin Rubber curing agents Coal powder
100 25 17.75 82
0.23 0.057 0.041 0.19
0.424 0.0812 0.036 0.244
0.06 0.06 0.1 0.16 0.05 0.053
0.014 0.0137 0.069 0.068 0.018 0.032
Changeable part Steel wool Iron powder Calcium carbonate Barite Iron oxide (magnetite) Iron oxide (limonite) a
26 26 45 70 22 23
Part per hundreds of rubber by weight.
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Table 2 Thermophysical properties of selected thermally conductive fillers Thermal conductivity (W/m C)
Copper Brass (70 Cu, 30 Zn) Aluminum Aluminum oxide Talc
394 111
8940 8520
383 385
204 33*
2700 3400**
896 760***
10.7
Density (kg/m3)
Specific heat (J/kg C)
Fillers
2.78
820
Ref.
[31] [32]
[32] [30]*, [33]**, [32]*** [17,34]
brass have the highest values of thermal conductivity, while the other two fillers show relatively lower values of thermal conductivity. The main reason to select these latter fillers is due to their performance in friction and thermal conductivity of composite materials. For instance, it has been reported that talc is more effective than copper in increasing thermal conductivity of polypropylene composite due to better interconnectivity of the talc crystals [17]. Moreover, aluminum oxide may be used as an abrasive powder in the friction materials [35]. 3.2. Formulation of the friction materials To enhance the thermal conductivity of the BM, the selected fillers are included into the compound. However, as the purpose of the present work is to obtain the conformable friction material, both the compressibility and frictional properties of the BM should be retained after addition of the fillers. To achieve these requirements, two constraints is accounted for in designing new materials including (1) the volume fraction of rubber component in formulations should not be less than a minimum value, i.e., 0.4; and (2) the amount of coal powder in formulations should be retained, i.e., 82 PHR, compared to the BM. Experimental results show that the compressibility of the friction materials is strongly influenced by the rubber volume fraction at a specified content of rubber curing system and phenolic resin. For the BM, when the volume fraction of SBR is kept higher than 0.4, the compression modulus of the friction material falls below 500 N/mm2 which is low enough to obtain a conformable friction material [22,36]. On the other hand, as coal powder is a low price material which controls the frictional properties of the friction material, we also keep unchanged PHR of coal powder in all new formulations. To design formulation of new friction materials, the composition of the BM in terms of PHR is considered as base formulation and then it is divided to two parts: (1) unchangeable part, which includes the rubber and its curing agents, phenolic resin and coal powder and (2) changeable part containing rest of components which are mainly the fillers. Table 1 illustrates these two parts of the compound. To satisfy the mentioned constraints, the new for-
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Table 3 The methodology used for preparing formulation of different friction materials containing copper in terms of PHR Ingredients
C-Cu-10
C-Cu-20
C-Cu-30
C-Cu-40
C-Cu-48
C-Cu-57
SBR 1502 Phenolic resin Rubber curing agents Coal powder
100 25 17.75 82
100 25 17.75 82
100 25 17.75 82
100 25 17.75 82
100 25 17.75 82
100 25 17.75 82
Calcium carbonate Iron powder Steel wool Barite Iron oxide (Limonite) Iron oxide (magnetite) Cu
1.3 26 26 70 23 22 43.7
0 0 9.5 70 23 22 87.5
0 0 0 36 23 22 131
0 0 0 0 15 22 175
0 0 0 0 0 0 212
0 0 0 0 0 0 300
Table 4 Formulation of different friction materials containing copper in terms of volume fraction Ingredients
C-Cu-10
C-Cu-20
C-Cu-30
C-Cu-40
C-Cu-48
C-Cu-57
SBR 1502 Phenolic resin Rubber curing agents Coal powder
0.445 0.085 0.038 0.256
0.447 0.086 0.038 0.257
0.456 0.087 0.039 0.262
0.469 0.089 0.04 0.027
0.48 0.092 0.041 0.276
0.459 0.088 0.039 0.263
Calcium carbonate Iron powder Steel wool Barite Iron oxide (limonite) Iron oxide (magnetite) Cu
0.002 0.014 0.015 0.071 0.033 0.019 0.021
0 0 0.005 0.071 0.034 0.019 0.043
0 0 0 0.037 0.034 0.019 0.065
0 0 0 0 0.023 0.02 0.09
0 0 0 0 0 0 0.111
0 0 0 0 0 0 0.15
mulations are obtained by replacing the fillers from changeable part of the base formulation with thermally conductive fillers. In order to reveal the effect of filler type on thermal conductivity of the friction material, only one thermally conductive filler is included in each formulation. However, to investigate the role of filler content on the thermal conductivity, different compounds with different contents of given filler are prepared. Table 3 presents the formulation of different friction materials containing various contents of copper and the methodology used to replace the fillers of BM with conductive fillers. In Table 3, each formulation containing copper is designated by C-Cu followed by two digits indicating the weight percent of copper. The same methodology is used for providing friction materials containing other conductive fillers. Table 4 gives formulations of Table 3 in terms of volume fraction calculated based on weight fractions. As seen, the volume fraction of rubber is higher than the limit value for all friction materials containing copper. Owing to different densities of conductive fillers, application of mentioned methodology for other fillers may be resulted in some friction materials with rubber content less than the limit value. 4. Experimental 4.1. Materials and preparation of specimens The ingredients of the base friction material indicated in Table 1 involve (1) polymers which are styrene butadiene
rubber (SBR 1502) from BIPC Co. (Iran) as polymer matrix and phenolic resin (Novolac IP 502) from Rezitan Co. (Iran); (2) curing agents of SBR including MBTS, zinc oxide, stearic acid and sulfur; and (3) fillers comprising coal powder, iron powder, steel wool, calcium carbonate, barite (barium sulfate), iron oxide (both magnetite and limonite). The physical properties of materials utilized in the BM are reported in Table 5. Copper powder, aluminum chips, brass chips, aluminum oxide and talc are used as thermally conductive fillers. All of the fillers employed in this investigation are supplied from local companies and are industrial grade. Table 6 illustrates the shape and particle size of these fillers. Two different sizes of brass chips are used to investigate the particle size effect. The specimens are prepared by mixing ingredients of each formulation using a two roll mill and then cured by a hot press at 150 C for 20 min. The cured specimens are then post cured at 180 C for 12 h and finally they are cut in desired dimensions. 4.2. Measurements 4.2.1. Thermal conductivity Thermal conductivity measurements are carried out under steady state condition, by utilizing the thermal conductance tester model TCM-1 (Mehr-Sanat Pajooh, Iran), which is based on the comparison method with small size specimen as explained in ASTM E1530. Disc shaped specimens with diameter of 50 mm and thickness of 10 mm are
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Table 5 Properties of ingredients used in the BM Fillers
Thermal conductivity (W/m C)
Density (kg/m3)
Comments
SBR 1502 Phenolic resin Coal powder Calcium carbonate Iron powder Steel wool Barite Iron oxide (limonite) Iron oxide (magnetite)
0.19–0.25 0.15 0.26 3 73.7 25 1.72* 5.1* 5.1
980 1280 1400 2700 7870 7750 4300** 3000** 5100
Bold faced value is used in calculations. Pure gum vulcanizate [37] Average value of casting resin [38] Ref. [39] Ref. [33] Ref. [31] Stainless steel 410 [40] Refs. [17,34]*; ** measured value *To be considered same as magnetite; **measured value Refs. [17,34]
Fillers
Particle size (lm)
Particle shape
Copper Brass chips I Brass chips II Aluminum chips Aluminum oxide powder Talc powder
30–65 (measured) 30–100 (measured) 100–450 (measured) 50–300 (measured) Very fine [17,34]
Spherical Platelet Platelet Platelet Platelet
Very fine (13–105 nm) [33]
Spherical or irregular
used in the instrument for thermal conductivity measurements. A known constant heat flux is applied from one side of the specimen. When the thermal equilibrium is attained and the system approaches to steady state situation, the temperature drop (DT) is recorded by K type thermocouples installed on top and bottom of the specimen. Knowing the values of heat flux, measured by heat flux transducer (HFT), temperature drop and thickness, the thermal conductivity can be determined by employing one-dimensional Fourier’s law of conduction. However, before performing the experiments for unknown specimens, HFT needs to be calibrated using two standard specimens with known thermal conductivities. The standard specimens used in this study are: Pyrex glass and stainless steel 304. All measurements are carried out approximately in the similar temperature range, i.e., 25–70 C. 4.2.2. Density The density of friction materials is determined according to procedure proposed in ASTM D792, which is based on Archimedes’ principle. 4.2.3. Optical microscopy In order to investigate the distribution of thermally conductive fillers in the composites and determine the particle size, an optical microscope model PME3 Olympus equipped to image analyzer software Omnimet Advantage (Buehler) is used.
against gray cast iron counter ring whose inner diameter is 300 mm. Friction tests are carried out under constant sliding speed of 700 rpm and braking pressure of 200 psi. After completion of the friction tests, the samples are weighed once again, and the cumulative weight loss is reported as specific wear in terms of volume. 4.2.5. Compressibility The elastic compression modulus of the friction materials as a measure of compressibility of the friction materials is measured using Rockwell hardness tester in accordance with methodology presented in UIC Code [41]. Details are given in [5]. 5. Results and discussion of the experimental data 5.1. Thermal conduction characteristics Fig. 1 shows variations of thermal conductivity of composite friction materials with volume fraction of conductive fillers. As shown in Fig. 1, in all cases, the thermal conduc-
7 BM Cu
6
Al Brass I Brass II
5
Al2O3 Talc
k (w/m.K)
Table 6 Particle size of the thermally conductive fillers
4
3 2 1 0
4.2.4. Frictional properties The friction tests are carried out on a small scale padon-ring type friction tester. Composite specimens with size of 27 mm · 25 mm · 5 mm are hydraulically pressed
0
0.05 0.1 0.15 0.2 0.25 Volume fraction of conductive filler
0.3
Fig. 1. Thermal conductivity of composite friction materials contained various thermally conductive fillers.
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tivity increases uniformly by increasing volume fraction of the conductive fillers. The results also show that thermal conductivity of the composite friction materials filled with thermally conductive fillers lies between 0.48 and 5.8 W/ m K, approximately up to 12 times increase in the effective thermal conductivity, depending on the type and content of the filler. Furthermore, the measured thermal conductivities are consistent with findings of other researchers [12,16,17]. From Fig. 1, it is found that the compound C-Al-40 containing aluminum chips shows the maximum thermal conductivity among all compounds (kC-Al-40 = 5.8 W/m C). This can be explained by relatively high thermal conductivity of aluminum (kAl = 204 W/m C) and its high volume fraction (which is around 25 vol%) due to its low density compared with copper which is 15% by volume in C-Cu-57. However, as shown in Fig. 1, at the same volume fraction, the thermal conductivity of copper filled friction material is slightly higher than the thermal conductivity of aluminum filled material. This behavior of thermal conductivity might be expected, because the thermal conductivity of copper is approximately twice the thermal conductivity of aluminum. As can be realized from Table 2, thermal conductivity of the selected conductive fillers is in the order as Cu > Al > brass > Al2O3 > talc. However as shown in Fig. 1, at the
same volume fraction, compounds filled with these fillers show different sequences as C-BrII > C-BrI C-Cu > C-Al > C-talc > C-AlO. This discrepancy in the thermal conductivity of the compounds can not be explained solely by the differences in the thermal conductivity of the fillers, but other parameters such as geometry of the filler and microstructure of the composite should be taken into consideration. As can be seen in Fig. 1, thermal conductivity of compounds filled with large size of brass chips (brass II in Table 6) is higher than the thermal conductivity of brass chips having small size (brass I in Table 6) at the same volume fraction. Furthermore, although the thermal conductivity of copper is approximately four times higher than the thermal conductivity of brass, the brass filled compounds show higher thermal conductivities than friction materials contained copper at the identical volume fraction. As the densities and specific heat capacities of these two fillers are approximately equal (see Table 2), this behavior can be attributed to the geometry of the fillers and microstructure of the composite. The particle size of the brass chips is larger than the copper (see Table 6). In addition, brass chips have platelet shape; while the copper particles are approximately spherical (see Fig. 2). In the platelet shaped fillers, the chance of creating partial interconnectivity among some particles increases, leading to higher thermal conduc-
Fig. 2. Optical micrograph of friction materials filled with thermally conductive fillers: (a) copper, (b) aluminum chips, (c) brass chips I and (d) brass chips II.
A. Shojaei et al. / Composites Science and Technology 67 (2007) 2665–2674
tivity of the composite [17]. On the other hand, as observed in brass chips filled compounds, thermal conductivity increases by increasing the size of platelet shaped fillers. These results emphasize that both shape and size of fillers have important role on thermal conductivity. Lower value of thermal conductivity of aluminum filled compounds with respect to compounds containing brass chips may be related to smaller size of aluminum chips (compared to brass II). In addition, other thermophysical properties of these fillers, i.e., density and specific heat capacity are different which may be regarded as source of the discrepancy observed in the thermal conductivity of the composite. Experimental data obtained in this study indicates that the fillers with larger size and platelet shape are more effective than the fillers with smaller size and spherical shape in enhancing the effective thermal conductivity of the friction material. Both talc and aluminum oxide are very fine particles and have the moderate thermal conductivities. Therefore, as shown in Fig. 1, compounds filled with these two fillers have the lower thermal conductivities among all compounds. However, despite lower thermal conductivity of talc with respect to aluminum oxide, talc filled compounds show relatively higher thermal conductivity. As reported by Weidenfeller et al. [17], platelet shape of talc may help to creating interconnectivity among the particles and this may be regarded as major source of higher thermal conductivity of talc filled compounds. 5.2. Physical and frictional characteristics Fig. 3 illustrates variations of measured density of friction materials with volume fraction of thermally conductive fillers used in this investigation. As seen in the figure, density of compound increases by increasing content of copper and brass from 1730 up to 2300 kg/m3. However,
Density (Kg/m^3)
2300 2200
BM Cu
2100
Al Brass I
2000
Brass II Al2O3
1900
Talc
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Table 7 Frictional properties and compressibility of thermally conductive friction materials Friction material
Coefficient of friction
Specific wear (cm3)
Elastic compression modulus (N/mm2)
Volume fraction of SBR in the compound
BM C-Cu-48 C-BrII-48 C-Al-48 C-talc-48 C-AlO-48
0.57 0.5 0.48 0.42 0.22 0.6
0.17 0.18 0.18 0.27 0.08 1
410 380 440 800 920 580
0.42 0.48 0.477 0.38 0.385 0.406
for aluminum, aluminum oxide and talc, the inverse behavior is observed, i.e., density of friction material decreases by increasing content of these fillers. This behavior can be clearly interpreted by the density of the filler. Low density fillers lead to low density composites and vice a versa. The friction, wear and compressibility of the friction materials are presented in Table 7. It is found that the specific wear and COF of the friction materials strongly depend on the conductive fillers used in the formulation. As the polymer matrix of all compounds is the same, therefore the observed difference in specific wear of different materials could be attributed to filler dependent mechanisms such as abrasive and adhesive mechanisms [42]. The highest changes in COF and specific wear with respect to BM belong to the aluminum oxide and talc filled compounds. However, experimental results presented here indicate that among all thermally conductive fillers copper powder shows relatively high and stable COF as well as low wear. Such frictional behavior has been reported for copper fiber filled phenolic resin based friction material [43]. Therefore, this filler seems to have a great potential to be used for producing thermally conductive railroad rubber-based friction materials. The compressibility of the friction materials depends on the rubber content. From Table 7, it is seen that the friction materials C-Al-48 and C-talc-48 have the higher compression modulus which have the lowest content of rubber. Of course, the filler can have a slight effect on compressibility. For instance, lower value of modulus for C-Al-48 with respect to C-talc-48 can be due to the fact that the aluminum is softer than talc. 6. Semi-empirical thermal conductivity model
1800
6.1. Development of the model 1700 1600 1500 0
0.05 0.1 0.15 0.2 0.25 Volume fraction of conductive filler
0.3
Fig. 3. Density of composite friction materials contained various thermally conductive fillers.
The geometric mean model for multiphase systems can be given as n Y / k c ¼ k /mm k /1 1 k /2 2 . . . k /n n ¼ k /mm ki i ð6Þ i¼1
where m indicates the continuous phase or matrix, n is the total number of dispersed phase or additives, ki and /i rep-
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resent the thermal conductivity and volume fraction of ith component, respectively, so that /m + /1 + /2 + + /N = 1. Based on Eq. (6), one can calculate the effective thermal conductivity of the composite if volume fraction and thermal conductivity of each component are known. As an example, the measured thermal conductivities of copper filled friction materials and the calculated ones based on Eq. (6) are illustrated in Fig. 4. From the figure, one can find that the model prediction and experimental data for the BM is in good agreement. However, by addition of copper, the measured values are deviated from the model prediction, and the deviation increases by increasing the copper content. More or less, similar results were also observed for other thermally conductive fillers used in this study. To predict the thermal conductivity of the composite accurately, Eq. (6) needs to be modified appropriately. To do this, for each dispersed phase distributed within a specific matrix, a corrected thermal conductivity is introduced as follows: ~k i ¼ F i ð/i Þk i ð7Þ where ~k i and ki are the corrected and real thermal conductivities of ith dispersed phase, respectively, and Fi(/i) is referred to filler correction coefficient which is generally function of volume fraction of the dispersed phase. Function Fi for an additive in a matrix can be a measure of indirect effects on thermal conductivity such as shape and size of filler as well as matrix–filler interaction. Such a correction coefficient in thermal conduction models has been proposed by many researchers [12,15,27]. Replacing the real thermal conductivities of dispersed phases with corrected thermal conductivities in Eq. (7), and rearranging the resultant equation leads to the following expression:
5 Calculated by Geometric mean model
k (w/m.K)
4
Experimental results
3
/
/2
/
k c ¼ F 1 ð/1 Þ 1 F 2 ð/2 Þ . . . F n ð/n Þ n k /mm
n Y
/
ki i
ð8Þ
i¼1
Eq. (8) may be expressed in a simple form as k c ¼ Að/1 ; /2 ; . . . ; /n Þk /mm
n Y
/
ki i
ð9Þ
i¼1
in which A is called overall correction function of conduction which is generally a function of volume fraction of the additives and might be determined from experimental results. 6.2. Application of the proposed model for composite friction materials It is somewhat difficult to obtain the function A based on Eq. (9) in the present form. For composite friction material studied in this work, one can make the following assumptions to simplify the proposed model: (1) The SBR rubber along with its curing system is considered as matrix, and other components are accounted for dispersed phases. (2) As was observed in preceding section, selected thermally conductive fillers have significant effects on thermal conductivity of the friction material, and alter considerably the thermal conductivity of the composite by alteration of their volume fraction. In addition, the presence of these fillers causes a strong deviation from the theoretical geometric mean model. Therefore, all fillers in the compound are divided to two groups, including thermally conductive fillers and non-conductive fillers. The non-conductive fillers in the BM do not deviate the thermal conductivity of the composite with respect to theoretical value. This can be found from the result presented in Fig. 4. According to this issue, we assume that the overall correction function of conduction is function of volume fraction of conductive fillers. Of course, it should be noted that correction coefficient of all non-conductive fillers appears as a mean constant value in function A and it is close to 1. According to assumptions presented above, and as only one conductive filler has been included in the materials, proposed model, i.e., Eq. (9), is simplified for friction materials as
2
1
k c ¼ Að/t Þk /mm k /t t
N Y
/
ki i
ð10Þ
i¼1
0 0
0.1 Volume fraction of Cu
0.2
Fig. 4. Comparison of calculated effective thermal conductivity of composite using geometric mean model and experimental data at different volume fractions of copper.
where subscript t represents the thermally conductive filler and N shows the total number of non-conductive fillers. According to simplified form of present model, i.e., Eq. (10), function A can be obtained based on experimental results presented in Section 5 as follows:
A. Shojaei et al. / Composites Science and Technology 67 (2007) 2665–2674 Table 8 Function A for compounds filled with thermally conductive fillers
Table 9 Formulation of different compounds containing combination of thermally conductive fillers in terms of volume fraction
Compound
Function A
C-Cu C-Al C-brass I C-brass II C-AlO C-talc
802.5/3 33.2/2 + 58.4/ + 1.125 55.9/3 32.7/2 + 8.1/ + 3.26 813.2/3 + 185.4/2 + 43/ + 1.9 1208/3 + 2772/2 + 246/ 0.939 6.4/2 + 3.1/ + 1.95 3.3/2 + 2.5/ + 2.65
Að/t Þ ¼
k ec /t Qn
k /mm k t
where k ec is the experimental thermal conductivity of friction materials. Using Eq. (11), value of A can be determined at each volume fraction of known conductive filler, from which one can express a functional form for A. According to this procedure, a series of polynomial functions is obtained for conductive fillers by using regression analysis and the results are presented in Table 8. 6.3. Development of the model for friction material containing more than one thermally conductive filler Eq. (10) can be applicable for friction material with one conductive filler. If more than one conductive filler is included in the friction material, according to assumption 2 mentioned above, Eq. (10) should be expressed as ! ! M N Y Y / / j k c ¼ Að/t1 ; /t2 ; . . . ; /tM Þk /mm k tj ki i ð12Þ j¼1
C-Cu/ Al-1
C-Cu/ Al-2
C-Cu/BrI/ Al-1
C-Cu/BrI/ Al-2
SBR 1502 Phenolic resin Rubber curing agents Coal powder Cu Aluminum chips Brass chips I
0.43 0.083 0.037
0.45 0.086 0.038
0.45 0.086 0.039
0.44 0.084 0.038
0.26 0.095 0.094 0
0.27 0.098 0.065 0
0.26 0.05 0.065 0.052
0.25 0.077 0.063 0.063
u
Að/t1 ; /t2 ; . . . ; /tM Þ ¼ Að/t1 Þ t1 Að/t2 Þ Að/tM Þ
Table 10 Comparison of measured and calculated thermal conductivities for different compounds filled with combination of thermally conductive fillers Compound
kmeasured (W/m K)
kcalculated (W/m K)
C-Cu/Al-1 C-Cu/Al-2 C-Cu/BrI/Al-1 C-Cu/BrI/Al-2
4 3.3 2.6 3.6
4.2 3.7 2.9 3.9
are presented in Table 9. The comparison between measured value and calculated one based on Eqs. (12) and (13) for each compound is given in Table 10. As can be seen, good agreement is observed in all cases, indicating the applicability of the proposed model to predict the thermal conductivity of the friction material. 7. Conclusions
i¼1
where M is the total number of thermally conductive fillers in the friction material. Determination of function A for such multi-conductive filler composite based on procedure mentioned for friction material containing one conductive filler is mathematically tedious and experimentally costly and time consuming. In such systems, we suggest the following model for function A as M Y
Ingredients
ð11Þ
/i i¼1 k i
¼
2673
ut M
ut
2
. . . Að/tM Þ
utM
ð13Þ
j¼1
where Að/tj Þ is overall correction function of conduction for a conductive filler as reported in Table 9, utj is the ratio of volume of jth conductive filler to total volume of conductive fillers in the friction material such that ut1 þ ut2 þ þ utM ¼ 1: Indeed, Eq. (13) is a geometric mean model based on A function of each filler and total volume of conductive fillers and it is called mean overall correction function of conduction. To verify the validity and applicability of the proposed model, some friction materials containing several conductive fillers are prepared and then their thermal conductivities are measured. The compositions of these compounds
Thermal conductivity of a rubber-based composite friction material has been studied in this investigation. Various thermally conductive fillers including copper, brass chips with two sizes, aluminum chips, aluminum oxide and talc have been selected and the effect of addition of these fillers on the thermal conductivity of the base friction material has been examined. It is found that the thermal conductivity of the friction material increases continuously by increasing the content of the selected fillers. Maximum thermal conductivity is related to aluminum chips filled compound due to higher volume fraction of this filler. However, at a given volume fraction, friction material containing larger size of brass chips shows higher thermal conductivity, which is a consequence of the shape and size of the fillers. Based on geometric mean model, a semi-empirical model of thermal conductivity is proposed for multiphase systems. In this model, the fillers are categorized into thermally conductive and non-conductive. To take into account the indirect effects of fillers on the effective thermal conductivity of composite, function A called overall correction function of thermal conduction is introduced for a system containing multi-non-conductive fillers and only one conductive filler. In addition, the model is extended to systems containing multi-conductive and non-conductive fillers, in which the
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correction function for such a system can be calculated based on function A of each thermally conductive filler obtained independently. Acknowledgements Authors are grateful to Mashin Lent Tehran Company, particularly Mr. Alaei who is general director of the company, to provide the materials and compounding machines used in this work. All the thermal conductivity measurements were carried out in Iran railway research center. The authors would like to express special thanks for their support. References [1] Gibson PA. Composition friction materials for the replacement of cast iron railway blocks. IMechE seminar publication on railway traction and braking; 1996. p. 75–85. [2] Jacko MG, Rhee SK. Brake linings and clutch facings. In: KirkOthmer (Ed.), Encyclopedia of chemical technology; 1987 [chapter 4]. [3] Takashi, Osamu N. Friction materials. US Patent 5576369; 1996. [4] Griffith AM. Composition railroad friction material with synthetic fiber content. US Patent 4217255; 1980. [5] Abbasi F, Shojaei A, Katbab A. Thermal interaction between polymer-based composite friction materials and counterfaces. J Appl Polym Sci 2001;81:364–9. [6] Panier S, Dufre´noy P, Weichert D. An experimental investigation of hot spots in railway disc brakes. Wear 2004;256:764–73. [7] Anderson AE, Knapp RA. Hot spotting in automotive friction systems. Wear 1990;135:319–37. [8] Dunaevsky VV. Prediction of railroad friction braking temperatures: prediction of average bulk and average surface temperatures of railroad wheels and brake discs. Tribol Trans 1991;34(3):343–52. [9] Limpert R. Brake design and safety. USA: SAE Publication Group; 1992. [10] Bijwe J. Composites as friction materials: recent developments in nonasbestos fiber reinforced friction materials – a review. Polym Comp 1997;18(3):378–96. [11] Shojaei A. A numerical investigation on the cure characteristics of railroad composite brake blocks during the compression molding process. Int Polym Process 2006;XXI:421–31. [12] Kusy RP, Corneliussen RD. The thermal conductivity of nickel and copper dispersed in poly vinyl chloride. Polym Eng Sci 1975;15(2):107–12. [13] Lu X, Xu G. Thermally conductive polymer composites for electronic packaging. J Appl Polym Sci 1997;65:2733–8. [14] Yu S, Hing P, Hu X. Thermal conductivity of polystyrene-aluminum nitride composite. Composites A 2002;33:289–92. [15] Mamunya YP, Davydenko VV, Pissis P, Lebedev EV. Electrical and thermal conductivity of polymers filled with metal powders. Eur Polym J 2002;38:1887–97. [16] Kumlutas D, Tavman IH, Coban MT. Thermal conductivity of particle filled polyethylene composite materials. Comp Sci Tech 2003;63:113–7. [17] Weidenfeller B, Hofer M, Schilling FR. Thermal conductivity, thermal diffusivity and specific heat capacity of particle filled polypropylene. Composites A 2004;35:423–9.
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