Referente Teórico

From the review of hot spotting theories, it was found that hot spotting can be driven by different mechanism and determinants. The main determinants studied in the published research are discussed in this section.

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Trigger conditions of hot spotting

As indicated by Dow and Burton (1972), Lee and Barber (1993) and Zagrodzki (2009), the traction force and shear stress due to sliding have insignificant effects on hot spotting based on both experiment and TEI models. In addition, the brake pressure was irrelevant on the number of hot spot according to the analytical prediction (Dow and Burton), FE simulation (Altuzarra, Amezua, and Aviles, 2002) and experiment (Kim, Cho and Kim, 2007). But the amplitude of the temperature variation and BPV correlated with the actuation brake pressure as indicated by Kim, Cho and Kim (2007).

Panier et al. (2005) argued that another trigger condition of hot spot was the energetic level which leads to the plastic yielding and the PWD phenomenon. In addition, Kamen and Dufrénoy (2012) investigated the correlation between hot spot distribution with braking energy level. It was found that at different energy levels, the hot spotting distribution showed different mechanisms. At lower energy levels, the hot spots were not evenly distributed, whereas the distribution was symmetric at higher energy levels. Similarly, Bryant, Fieldhouse and Claffey, (2013) stated that the number of hot spots was influenced by the amount of energy input as it was observed that during the cooling phase after the brake test, the order of deformation decreased compared with the in-stop period. This indicated that the residual stress in the disc due to manufacturing was released and facilitated the thermal deformation when considerable heat was generated during braking.

Disc and pad geometry

Through both experiment and simulations, Zagrodzki and Truncone (2003), and Zagrodzki (2009) found that geometric imperfections (such as DTV) were the determinants of the excitation of the hot spotting, but the hot spotting can be

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triggered without geometric imperfection as well. It implied that the hot spotting mechanisms for perfectly flat solid disc and ventilated disc were different. Bryant, Fieldhouse and Talbot (2011) found that the number of hot spot was correlated to the vent number (see Figure 1.2) for the ventilated disc in some instances. As the number of hot spot for solid disc was mainly determined by the speed according to the TEI theory, the findings of Bryant, Fieldhouse and Talbot (2011) implied that the hot spotting of ventilated and solid discs could be different.

In addition, both TEI predictions (Lee and Barber, 1993) and experiments (Steffen, 2006) indicated that a higher diameter-thickness ratio with constant energy input could lead to a higher maximum temperature and temperature variation.

Moreover, Eltoukhy and Asfour (2008) suggested reducing the pad arc length to prevent hot spotting which agreed with Panier, Dufrénoy and Weichert (2004) in their simulations and the TEI theory (Lee and Barber, 1993) that the decrease of the pad length generated more hot spots but the pad length should be longer than the minimal hot spot waviness to trigger hot spotting (Lee and Barber, 1993). However, Sardá et al. (2008) argued that the pad arc length was not the determinant of number of hot spot but the reduction of pad arc length could slightly decrease the peaks temperature and the temperature variations between peaks.

Material selection

In order to reduce the temperature magnitude and variation during hot spotting, material properties of disc and pads were investigated by previous researchers.

In order to achieve more uniform contact pressure distribution to reduce the thermal gradient, it was suggested that lowering the compressive stiffness or

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Young’s modulus of the pad would be successful (Jacobsson, 2001 and 2003, Thuresson, 2004, Shahzamanian et al., 2010, and Cho et al. 2012). Regarding the disc Young’s modulus, Kao and Richmond (1994) indicated that the influence was insignificant. Another strategy to provide uniform contact pressure was lowering the thermal expansion coefficient according to Jacobsson (2001 and 2003) and Kao and Richmond (1994). Moreover, Zagrodzki, and Truncone (2003) stated that the Poisson’s ratio had little influence on the TEI solutions. Regarding the reduction of the radial hot band migration, Graf, and Ostermeyer (2014) indicated that the Young’s modulus of the pad should be increased.

In addition, since lower the temperature at the contact interface can also reduce the thermal gradient. Thus increase specific heat capacity and conductivity of the pad were suggested by Jacobsson (2001 and 2003) and Eltoukhy, and Asfour (2008). However, Cho et al. (2012) argued that hot spotting was not sensitive to pad conductivity and Kao and Richmond (1994) and Graf, and Ostermeyer (2014) indicated that the conductivity should be reduced to prevent hot spotting.

Furthermore, as suggested by Barber (1969) and Kao and Richmond (1994), wear has cancelling effects to thermal localisation which implied that improving the wear rate of the friction material can promote a reduction in the hot spotting. Thuresson (2004) indicated that the lower heat generation could be achieved by reducing the coefficient of friction.

Even though the main effects of various material properties were studied, it can be found that the interactions between the materials properties have not been investigated. The effects of material properties on the radial hot band migration were not focused upon.

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Uneven wear

Barber (1967) investigated the linkages between hot spotting and wear volume and found that thermal distortion resulting in temperature and contact pressure localisations was the main source of wear. Furthermore, Barber (1969) indicated that the stability of the thermo-elastic contact was determined by the relationship between thermal expansion and the wear rate which had positive and negative effects on contact pressure localisation respectively. To be specific, thermal localisations can be boosted by thermal expansion but reduced due to wear.

To investigate the distribution of wear and interface heat transfer, Day and Newcomb (1984) and Day, Tirovic, and Newcomb (1991) used finite element analysis to incorporate wear and thermal expansion effects. The results revealed good correlation between temperature, pressure and wear volume distribution in the radial direction as shown in Figure 2.10. Similarly, by implementing 3D scanning techniques, Fieldhouse and Beveridge (2010) found that the wear volume at the locations of hot spots was greater than surrounding areas resulting in concave regions after cooling.

Figure 2.10 Temperature, pressure, and wear distribution on friction surface (Day and

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Regarding hot band migration, Ostermeyer and Graf (2013) presumed that wear was the trigger of hot band migration and performed a two-rods-against-wall numerical model to verify. Wear, friction heating and thermal expansion effects were considered. It was found that wear significantly correlated with the periodicity of contact pressure within the two contact rods.

Uneven cooling

According to Jacobsson (2001), uneven cooling is another source of temperature variation. As convection accounts for ~40% to 80% of all heat dissipation from the brake disc (Tirovic, 2013), the cooling effect is significant in hot spotting research. In addition, Panier et al. (2005) indicated that some regional hot spots were areas with low thermal gradients on the whole surface of the disc due to inhomogeneous cooling. Similarly, Bryant, Fieldhouse and Talbot (2011) indicated that the proper design of the cooling channel of ventilated discs can significantly reduce the temperature variations.

Wu et al. (2008) investigated the nature of convective cooling due to the vibrational excitation for a metal plate. The results showed significant enhancement in cooling performance due to the high frequency vibration, but in the frequency range of hot judder (<1kHz) the improvement was insignificant.

Yi and Bendawi (2012) investigated the linkage between cooling effect and TEI using the 2D FE method. It was found that the convective cooling coefficient had no effect on the number of hot spot at the lowest critical speed, whilst it significantly affected the critical speed of higher order hot spotting. Therefore, the authors argued that the previous TEI researchers overestimated the critical speed due to inappropriate modelling of heat convection.

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Other determinants

As indicated by Bryant, Fieldhouse and Talbot (2011), both thermo-elastic and thermo-plastic effects can affect hot spotting process. After the plastic yielding occurred, hot spots were more likely to be triggered at identical locations since the disc surface ripples from thermoplastic deformation cannot be removed after cooling. By using Scanning Electron Microscopy, Kasem et al. (2011) found that the hot (blue) spot locations on the disc surface were relatively irregular and rougher than the surrounding smoother locations. Therefore, it can be presumed that the disc circumferential roughness variation can affect the formation of hot spots by introducing a friction coefficient variation, contact pressure variation and subsequent heat flux variation.