Influence of wear on thermoelastic instabilities in automotive brakes

doi:10.1016/j.wear.2013.09.009

Wear

Volume 308, Issues 1–2, 30 November 2013, Pages 113-120

https://doi.org/10.1016/j.wear.2013.09.009 Get rights and content

Highlights

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We introduce two new models on the interaction of thermoelastic instability (TEI) and wear: one minimal model and one model with many DOF.
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The minimal model shows different solution regimes: a periodic solution can only be found if wear is included.
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A nonlinear analysis shows that every unstable solution is a periodic solution.
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The results of the model with many DOF agrees with experimental results on the “Migrating Hot Band” phenomenon in brake systems.

Abstract

In typical automotive disk brakes, two pads of organic material slide against both surfaces of a gray cast iron disk. The two materials have contrary properties with regard to elasticity, temperature and wear. One aim of this is to avoid thermoelastic instabilities (TEI) that lead to material disruption and vibrations. TEI results from local thermal expansion at regions of elevated temperature, which increases local contact pressure and destabilizes the temperature field. Common TEI models scarcely account for wear. To investigate TEI, a multi-field-problem (temperature and elastic field) must be solved. Wear can be included via boundary conditions, in terms of time-dependent contact topography and load-distribution. The basic interaction mechanisms between wear, temperature and elasticity can be explained by a minimal model that allows a nonlinear investigation and a multi-DOF-model. The inclusion of wear results in a periodic movement of hot bands that influence the effective braking radius. A nonlinear analysis shows that this periodicity is possible, although a linear model computes purely real eigenvalues. A comparison with experiments indicates that the correct stability threshold and the correct eigenform are found. The presented approach shows how wear influences the dynamics of TEI, and that a periodic motion of TEI is possible if wear is taken into account. This can only be partially described by linear models because it is highly nonlinear (local loss of contact). The approach focusses on automotive brakes, but can similarly be applied to clutches or disk brakes with multiple disks, e.g. in aircraft.

Introduction

The contact in automotive disk brakes is typically of a brake pad with more than ten ingredients sliding against a gray cast iron disk. The mechanical energy dissipated in the boundary layer between pad and disk is transformed into heat and plastic deformation, which results in wear of the contacting bodies. The generated heat is conducted into both bodies: pad and disk. It has been observed in many experiments that the rise in temperature is not always homogenously distributed over the contact surface [4], [1], [9]. At high sliding velocities, the sliding bodies show local material disruptions, which arise from local temperature maxima [2]. The resulting classical patterns are known as “hot bands” and “hot spots”. Hot bands are rings of elevated temperature on the brake disk. The width of this ring is considerably less than the width of the pad. Hot spots describe the maxima of a temperature field that periodically occur around the circumference of the disk. Investigations that show thermal measurements of both phenomena are published in [19].

The occurrence of local thermal maxima can be mathematically understood as instabilities of the temperature field. A disturbance that locally increases in the temperature field leads to a local rise in material volume due to thermal expansion. At such a position, the surface area slightly bulges and carries a greater frictional load in the contact between pad and disk. This mechanism has been described first in [4] and is known as a “thermoelastic instability” (TEI). Many models are available today that describe different aspects of TEI by finite element models e.g. [23], [22] or analytical approximations, e.g. [14], [13], [8].

One phenomenon frequently observed in experiments, but still lacking a deeper and fundamental model-based investigation, is the occurrence of migrating hot bands [15], [10]. These hot bands are not fixed, but slowly propagate from the inner radius to the outer radius and back again. Furthermore, the splitting and unification of hot bands have been observed [6]. Fundamental experimental investigation of the migration of hot bands was carried out by [21], [12]. Experiments have shown a clear link between the time-dependent radial position of a hot band and the time-dependent braking torque. Because the hot band carries the majority of the global frictional load, the average frictional radius is nearly identical with the position of the hot band. To avoid periodic braking torques, the motion of hot bands must be suppressed.

Only a minority of the models for hot bands are capable of describing their movements. Few publications suggest models for the motion of hot bands. Dow and Burton [7] studied a linear model of a wear-exposed blade sliding over a body. The model shows an unstable solution with a periodic component. Because infinite amplitudes and traction forces between the sliding bodies are allowed, no steady-state solution is found. Publications on TEI that allows for a local loss of contact typically involve a steady-state solution of the disturbed temperature fields, but those models do not include wear [24], [20]. Kao and Richmond [11] investigated a two-dimensional model of a disk brake by FEM simulation in time domain. By adding wear, they found a time dependency of the position of the temperature maximum, but the computation time is too short to cover a full hot band migration cycle. For basic investigations, a minimal model that finds a link between wear and the motion of hot bands was suggested in [16].

The present work covers a systematic investigation of a minimal model for hot band motion. This minimal model is discussed linearly and nonlinearly by including a possible loss of contact between pad and disk. Additionally, the model is expanded to a multi-DOF model that is compared with experiments.

Section snippets

Basic equations

The model under investigation is shown in Fig. 1. Inspired by [16], [18], it consists of two rods with length h and quadratic surface area A. These rods represent two neighboring regions in the sliding contact area. The two rods both have the same materials properties: Young's modulus E, thermal expansion α, thermal conductivity λ, heat capacity c and density ρ. While one end of each rod stands on a rigid, nonconductive foundation, the other end is pressed with global normal force N_glob against

Nondimensional formulation

The only relevant solutions are those where the disturbances have opposite signs for both rods [18]. The number of degrees of freedom of the systems can therefore be reduced by introducing a constant reference solution. $T_{1} = T_{r e f} + T T_{2} = T_{r e f} - T u_{1} = u_{r e f} + u u_{2} = u_{r e f} - u N_{1} = 0.5 N_{g l o b} + N N_{2} = 0.5 N_{g l o b} - N$

The system can further be transformed using nondimensional quantities $\bar{T}$ , $\bar{u}$ and $\bar{N}$ for system states and dimensionless time $\bar{t}$ . $T = \bar{T} \cdot \tilde{T} u = \bar{u} \cdot \tilde{u} N = \bar{N} \cdot \tilde{N} t = t \cdot \tilde{t}$

The time derivatives are therefore expressed by $\overset{\cdot}{(\cdot)} = \frac{d (\cdot)}{d t} = \frac{d (\cdot)}{d}$

Linear investigation

Only for small amplitudes, it can be assumed that there is no loss of contact, and Eq. (12) reads $[\begin{matrix} \bar{T} \\ \bar{u} \end{matrix}]' = [\begin{matrix} \bar{v} - 1 & \bar{v} \\ - \bar{v} \bar{w} & - \bar{v} \bar{w} \end{matrix}] [\begin{matrix} \bar{T} \\ \bar{u} \end{matrix}] .$

The complex eigenvalues, $\bar{D}$ , of the matrix in Eq. (18) provide information about time behavior: stability and periodicity. The stability chart is shown in Fig. 2.

Four different stability and periodicity regions appear. It is clear that the stability threshold between region 2 and region 3 in Fig. 2 is barely influenced by wear, which only leads to a weak

Nonlinear investigation

A numerical integration of Eq. (12) indicates that for the instability region of the origin, the solution converges to a limit cycle when local loss of contact is assumed. This is because the instability is based on a load transfer from one rod to the other. This load transfer reaches its maximum when one rod loses its contact. For cases without wear, the interaction of TEI and local loss of contact has been analyzed numerically in [24], [20]. Because a numerical integration is rather

Reference experiment

The analyzed minimal model with two rods shows basic effects of the interaction of wear and TEI. In order to describe migrating TEI and a local loss of contact, a discrete model with multiple DOF is required. The model proposed in the present investigation is motivated by the experiments of Kleinlein [12]. In his experiments, the pad material fully covers the steel disk and rotates against this disk in a drag test with constant angular velocity at low contact pressure. The velocity was

Model definition

The following derivation of the model is analogous to the derivation of the minimal model, Eqs. (1), (2), (3), (4), (5), (6), (7). A setup as shown in Fig. 6 is assumed: Two disks fully contact each other; they are pressed together with force N_glob and rotate against each other with angular velocity ω. One disk is made of steel (index “D”), the other is made of a frictional pad material (index “P”). The system is formulated in cylindrical coordinates. In analogy to the minimal model discussed

Results

Eqs. (24), (25), (26), (27), (28), (29) are numerically integrated while the angular velocity is increased every 12 h simulation time in the following steps: $ω = 100 rpm, 125 rpm, 150 rpm, 175 rpm, 500 rpm$ . The overall dynamics can be globally discussed in terms of the resulting braking torque $M_{B} = \sum_{i j} r_{i} N_{i j}$ , as shown in Fig. 7.

For 100 rpm and 125 rpm, a stable sliding process is observed, while for 150 rpm and 175 rpm, periodic braking torques appear. The frequency of the hot band is approximately $1.3 \times 10^{- 3} Hz$ ,

Notes on the transfer on automotive brake disks

The material couple for brake pad and disk, and their respective parameters applied in the present study are similar to those in automotive disk brakes. In contrast, the geometry of the system studied above differs from that of a disk brake. Typically, the circumference of a brake disk is only partially covered by the pad, not fully covered as was shown in these analyses. This has two consequences.

Heat, which is the destabilizing component in TEI, is only generated in a fraction of the disk

Conclusion

Wear can be the driving mechanism behind the migration of the temperature maximum of a thermoelastic instability, especially of a hot band. Two models have been applied in order to study this phenomenon: A minimal model with a limited number of DOF and a multi-DOF-model. The presented model-based investigations cover only few, although the most important aspects influencing the dynamics of the system under research, as follows: heat generation, thermal expansion, thermal conduction and material

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Influence of wear on thermoelastic instabilities in automotive brakes

Highlights

Abstract

Introduction

Section snippets

Basic equations

Nondimensional formulation

Linear investigation

Nonlinear investigation

Reference experiment

Model definition

Results

Notes on the transfer on automotive brake disks

Conclusion

Wear

Wear

Wear

Wear

Effect of intermittent contact on the stability of thermoelastic sliding contact

J. Tribol.

Thermoelastic instabilities in the sliding of conforming solids

Proc. R. Soc.

IR-camera methods for automotive brake system studies

Proc. SPIE

The role of wear in the initation of thermoelastic instabilities of rubbing contact

J. Lubr. Technol.

Hot bands and hot spots: some direct solutions of continuous thermoelastic systems with friction

Phys. Mesomech.

Development of a high speed system for temperature mapping of a rotating target

Proc. SPIE

Frictionally excited thermoelastic instability and the suppression of its exponential rise in disc brakes

J. Therm. Stresses