1
INFLUENCE OF MECHANICAL PARAMETERS ON THE TRIBOLOGICAL AND THERMAL BEHAVIORS OF STEEL-COMPOSITE
CARBONE/CARBONE COUPLE
Abdeldjalil BENFOUGHAL1,2, Khaled BOUBENDIRA1, Nasira SASSANE1, Mohamed BOULKRA1, Skander BOUKHEZAR1, Noureddine BOUGHDIR1, Nihel HAMZAOUI1
1Research Center in Industrial Technologies (CRTI), P.O.Box 64 Cheraga 16014.Algiers.ALGERIA
2Faculté des sciences de la technologie, Laboratoire de Mécanique Campus Chaâbat- Erssas, Université des frères Mentouri, Constantine 25000 ALGERIE
Abstract: The tribological and thermal behavior of dry sliding contact steel composite carbone/carbone and steel-organic matrix composites are studied according to the parameters normal load, sliding speed, friction coefficient and test time. In the case of automotive braking, using a mathematical model, the surface temperature of contact was determined. Four normal forces, four sliding speeds and four friction coefficients were applied in this study. These parameters have a significant influence on the variation of average contact temperature. The results illustrate the evolution of the contact temperature according to the braking time.
Key words: Temperature, Friction, Steel, Composite, Disc, Trim.
Nomenclature
𝛼 : Coefficient of generation of flow (without dimension) 𝛿 : Height of the asperities [m]
𝜙 : Heat flow [W]
𝜑 : Surface heat flow [W.m -2] 𝜆 : Thermal conductivity [W.m-1.K-1] 𝜇 : Friction coefficient (without dimension) 𝜌 : Densité [kg.m-3]
a: thermal diffusivity [m2.s-1]
c: mass calorific capacity [J.kg-1.K-1]
2 d, e: thickness [m]
P: contact pressure [N.m-2] q: voluminal heat flow [W.m -3] t: time [s]
𝐴 : the real contact area [m2]
𝐴𝑎 : the apparent contact area [m2]
tf: braking time [s]
S: surface [m2] T: temperature [°C]
T0: initial temperature [°C]
V: speed [m.s-1] d: disc
g: trimming INTRODUCTION
The contact is a multi-field field. Indeed, it calls upon the fields of mechanics, friction, the behavior of materials and thermic. It is moreover a going problem multi-scales of the microscopic effects (third bodies, tribological transformations of surfaces, etc.) with the macroscopic phenomena of dissipation of structural heat or deformation, etc.
Many applications require the comprehension of the phenomena taking place within the contact.
Among them, in the systems mechanics, one can quote the brakes, the clutches, the gears, etc.
Braking is a significant field and much studied last years. One finds the brakes in many applications such as the car, the railway one, aeronautics but also in the industrial world. The major mechanism which controls the dimensioning of the disc is the thermal phenomenon of dissipation which it is a question of controlling well.
The local rise in the temperature which results can strongly affect the properties of surface of materials in dynamic contact.
The physical phenomena brought into play in braking have a character multi-scale, macro scales of the system and components until the scales micro of the contact, and character multi-physics, implying many disciplines such tribology, the science of materials, thermomechanics and vibro- accoustics [1].
A composite material of friction to organic matrix conceived for applications of railway the braking type is typically made up:
3
- Fibers which give to material its mechanical properties, thermal and tribological [2, 3, 4],
- Particles which improve the coefficient of friction by increasing it (abrasive particles) and by stabilizing it (lubricating solids), which modify the thermal properties and which limit wear [5], - Of a matrix which ensures the cohesion of the unit.
The objective of this article is to study the change of the temperature in a dynamic contact dry steel- composite carbon-carbon and steel-composite with organic matrix and to make a comparison of the thermal behavior between the two couples.
II.DESCRIPTIONOFTHEPROBLEM
A disc brake is composed of several elements. The study from a thermal point of view initially requires simplifying the problem. Indeed, the rise in temperature of a brake is mainly due to the contact rubbing between the disc and the trimmings. One will not take into account that these two elements in the thermal analysis (figure 1).
The setting in equation of these problem, eminently transitory, remains rather complex. The system is subjected, mainly with two phenomena: conduction and convection. The equation of heat leads to the following formulations, in a cylindrical frame of reference (figure 2).
Figure 1. Definition of problem [6]
∂Td
∂t = ad[∂2Td
∂r2 +1 r
∂Td
∂r + 1 r2
∂2Td
∂θ2 +∂2Td
∂z2 ]
rintd ≤ r ≤ rextd , 0 ≤ θ ≤ 2π, −e2d ≤ z ≤e2d (1)
∂Tg
∂t = ag[∂2Tg
∂r2 +1 r
∂Tg
∂r + 1 r2
∂2Tg
∂θ2 +∂2Tg
∂z2]
rintg ≤ r ≤ rextg , θ1 ≤ θ ≤ θ2, −e2d ≤ z ≤e2d, −eg≤ z ≤ −e2d
Two types of conditions limit are defined:
4
- conditions of exchange by convection with the external environment;
- a condition of generation of heat by friction on the level of the zone of contact.
For the convective phenomenon, one a:
- For the disc:
−λd∂T∂zd = h1Td(r, θ, ±e2d) , rintd ≤ r ≤ rextd , θ2 ≤ θ ≤ θ1 (2) rintd ≤ r ≤ rintg et rextg ≤ r ≤ rextd , θ2 ≤ θ ≤ θ1
−λd∂T∂rd = h2Td(rextd , θ, z), 0 ≤ θ ≤ 2π, −e2d≤ z ≤e2d (3) - For the trimming :
−λg∂T∂zg = h3Tg(r, θ, ± [e2d+ eg]), rintg ≤ r ≤ rextg , θ1 ≤ θ ≤ θ2 (4)
−λg∂T∂θg = h4Tg(r, {θ1
θ2, z), rintg ≤ r ≤ rextg , −eedg−ed2≤z≤−edd
2≤z≤eg+edd (5)
−λg∂T∂rg = h5Tg({rintg
rextg , θ, z), θ1 ≤ θ ≤ θ2,
ed2≤z≤edd+eg
−(ed2+eg)≤z≤−edd (6) With regard to the generation of heat by friction, there is the following formulation:
−λd∂T∂zd = φd(r, θ, ±e2d),
−λg∂T∂zd= φg(r, θ, ±e2d) (7)
Where φd+ φg = φt
With φt the total flow generated by friction.
It is noted easily that the analytical resolution of this type of problem is complex. Many authors endeavored to determine the levels of temperatures reached on the surface of friction. They more or less made assumptions concerning the flow of heat in the solids in contact but also on the convection.
The model more used is that of Newcomb. This study considers a perfect contact between the disc and the trimming.
III.ANALYTICALSOLUTION
Model of Newcomb
In its study, Newcomb [7] considers an one-way flow of heat through four infinite surfaces modeling the contact between a disc thickness d1 and two trimmings thickness d2.
5
∂2T1
∂x2 − 1 λd
∂T1
∂x = 0, 0 < 𝑥 < d1, t > 0
∂2T2
∂x2 −λ1
g
∂T2
∂x = 0, −d2 < 𝑥 < 0, d1 < 𝑥 < d1 + d2, t > 0 (8) Surfaces x =d1+d2 and x = - d2 are the free faces supposed insulated.
∂T2
∂x = 0, x = −d2, x = d1+ d2, t > 0 (9) Surfaces x = 0 and x = d2 are subjected to a surface heat flow resulting from the contact rubbing between the disc and the trimming (figure .2).This surface flow Q is considered linearly decreasing with time and of value q = q0(1 −tt
f) where q0 is the value of surface flow at the moment t=0.
ag∂T2
∂x = −q2, x = 0, x = −d1, t > 0
ad∂T∂x1 = −q1, x = 0, x = −d1, t > 0 (10)
q = q1+ q2, T1 = T2, x = 0, x = d1, t > 0
Figure 2. Diagram of the model of Newcomb [7]
The resolution, by the transform of Laplace, of the equation of heat coupled with the conditions limit adiabatic in x = -d2, x = d1 + d2 as has the condition of temperature equal to the level of the contact (T1 = T2 = Ts) gives the following relation for the temperature of surface (X = 0 and X = d2) [6]:
Ts= T0+λq0ad1 2⁄
d(1+σ){2tπ1 21 2⁄⁄ (1 −23tt
f) +(1+σ)4t1 2⁄ [(ierfc(2kd)) − σ. ierfc(2kg) − 4tt
f(i3erfc(2kd) − σ. i3erfc(2kg))] + 2(1 − 2A2)t1 2⁄ [ierfc(2(kd+ kg)) − 4tt
fi3erfc(2(kd+ kg))] + 4Bt1 2⁄ [ierfc(4kd) − σ. ierfc(4kg) − 4tt
f(i3erfc(2kd) − σ. i3erfc(2kg))] + 2(1 + 3A − A2)t1 2⁄ [ierfc(2(2kd+ kg)) − 4tt
fi3erfc(2(2kd+ kg))] + 2(1 − 3A − A2)t1 2⁄ [ierfc(2(2kd+ kg)) − 4tt
fi3erfc(2(2kd+ kg))] + 4Ct1 2⁄ [ierfc(6kd) − 4tt
fi3erfc(6kg)] + ⋯ . . } (11)
6
It is significant to note that several studies [8, 9] use another form of the equation of Newcomb; this formulation is obtained starting from the equation (11) in which only, the first part of the second member is retained:
Ts= T0+λq0ad1 2⁄
d(1+σ){2tπ1 21 2⁄⁄ (1 −23tt
f)} (12)
The use of this equation is subjected to the checking of the following condition [9]:
Γ =2.(ad1
1.tf)0.5≥ 1,21 (13) A- Materials
The materials constituting the disc and the trimmings are respectively, steel, a composite with organic matrix and a composite carbon-carbon, whose physical properties are given in Table 1.
Table 1. Properties physiques for disc and trimming
B- Application for automobile brake
In order to be able to compare the temperatures of surface reached when the load is varied, the case of an automobile disc brake will be studied. The principal facts of the case are as follows (Table
2):
Table 2. Data of studied braking
Diameter external of the disc (mm)
Diameter internal of the disc
(mm)
Time of braking (s)
Ambiant Temperature (°C)
227 132 6 20
Disque (Acier)
Trimming (composite)
Trimming (composite c-c)
Thermal conductivity (W. m−1. K−1) 43,5 12 30
specific heat capacity (J. Kg−1. K−1) 445 900 1420
Density (Kg. m−3) 7850 2500 1800
7 IV.RESULTSANDDISCUSSION
Braking constitutes an application of the dry contact rubbing. The discs of brake suffer severe damage having milked with thermic (cracking resulting from thermal tiredness, etc). So of many works [8, 10] were undertaken in order to better include/understand and control the evolution of the temperatures reached with the contact. All the theoretical studies considered the case of perfect contact between disc and trimming. The contribution of numerical made it possible to take into account geometries and conditions more realist than for the analytical models.
It is consequently noticed, at the beginning of breaking that, the contact temperature increases according to time up to a maximum value, and then it tends to be stabilized. This stabilization is due probably to the reduction number of revolutions of the disc because of braking.
The increasing of contact temperature reached is due to the presence of debris trapped between the disc and the trimmings plows surfaces of contact and make severe deformation at the interface.
Adhesion and abrasion are mechanicals wear dominant in this case. The sliding wear and applied load increase the contact temperature due to the friction heat.
The increase in the temperature depends on the load, sliding speed and friction coefficient, indeed, the maximum temperature varies from 165 to 255 °C approximately for sliding speed going from 100 to 160 Km/h for the couple steel/composite carbon-carbon. On the other hand, for the couple steel/composite with organic matrix the temperature varies from 190 to 290 °C for the same conditions.
Figure 3. Evolution of contact temperature for the couple: (a) steel- composite carbon-carbon, (b) steel- composite organic matrix according to time: p = 10 KN and 𝜇 = 0,27.
0 1 2 3 4
0 30 60 90 120 150 180 210 240 270
V=100Km/h V=120Km/h V=140Km/h V=160Km/h
Temperature[°C]
Time[s]
8
Figure 4. Evolution of contact temperature for the composite couple steel- composite organic matrix according to time: p = 10 KN and 𝜇 = 0,27.
Figure 5 shows that the contact temperature increases quickly for the couple steel-composite with organic matrix that for the couple steel-composite c-c. In addition, one also notices that, the evolution in contact temperature for the same conditions between the two material couples varies until tf = 2 s, then, it is stabilized for a value of ΔT ≈ 30 °C.
Figure 5 shows the influence of the couple of materials on the thermal behavior. Indeed, one can note that the couple steel/composite c-c tolerates the temperature better that the couple steel/composite with organic matrix, and this because the thermal properties of carbon, which support the thermal changes very well.
Figure 5. Evolution of contact temperature versus time with p = 10 KN, V = 27,77 m/s and 𝜇 = 0,27.
0 1 2 3 4
0 30 60 90 120 150 180 210 240 270 300
Temperature[°C]
Time[s]
V=100Km/h V=120Km/h V=140Km/h V=160Km/h
0 1 2 3 4
0 30 60 90 120 150 180 210
Temperature [°C]
Time [s]
Steel- composite c-c
Steel- organic matrix composite
9
CONCLUSION
We developed in this article a study intended for the determination of the interfacial temperature of a dry dynamic contact.
The presence of the third body is probably one of the most influential parameters on the level of average contact temperature, in particular, by the surface of the trimming.
The results obtained show that the most influential parameters on the variation in the temperature are: the sliding speed and the nature of materials used.
One can note that the couple steel/composite c-c tolerates the temperature better that the couple steel/composite with organic matrix, and this because of the thermal properties of carbon, which support the thermal changes very well.
We can conclude that the interfacial temperature plays a paramount role in the tribocontacts.
REFERENCES
[1] Anne-Lise Bulthé, Caractérisation expérimentale du contact frottant disque garniture sous sollicitations sévères de freinage. Prise en compte des interactions tribologie, thermique et physico-chimie, thèse de doctorat, Université des Sciences et Technologies de Lille Novembre 2006.
[2] Satapathy B.K., Bijwe J., Performance of friction materials based on variation in nature of organic fibres. Part 1 Fade and recovery behaviour, Wear 257 (2004) 573-584.
[3] Jang H., Ko K., Kim S.J., Basch R.H., Fash J.W., The effect of metal fibers on the friction performance of automotive brake friction materials, Wear 256 (2004) 406-414.
[4] Ho S.C., Chern Lin J.H., Ju C.P., Effect of fiber addition on mechanical and tribological properties of a copper/phenolic-based friction material, Wear 258 (2005) 861-869.
[5] Kato H., Severe-mild wear transition by supply of oxide particles on sliding surface, Wear 255 (2003) 426-429.
[6] Didier MAJCHERCZAK, Etude thermique d’un contact glissant : Approche numérique et expérimentale, thèse de doctorat, Ecole polytechnique et universitaire de Lille, 25 Septembre 2003.
[7] T.P. Newcomb; Transient temperature attaint in disk brakes; British Journal of Applied Physics; Vol. 10; 1959; pp. 339-340.
[8] R. Limpert; Brake design and safety; Edition Elsevier; 1992.
[9] O. Roussette, Y. Desplanques, G. Degallaix, Y. Gallo et P. Petit ; Essais tribologiques représentatifs d’une sollicitation thermique de surface très sévères en freinage ferroviaire ; Journées européennes du freinage ; 2002 ; pp. 339-350.
[10] T. P. Newcomb and R. T. Spurr; Braking of road vehicules; Chapman and Hall Ltd; 1967.
