An Eulerian approach for simulating frictional heating in disc-pad systems

Strömberg, Niclas

doi:10.1016/j.euromechsol.2011.04.004

Cited by 16 publications

(13 citation statements)

References 24 publications

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“…If the speed of convection is high, some kind of stabilization is required. In the in-house software a streamline-upwind approach is adapted to stabilize the solution [26]. In this implementation, the contact pressure is not constant, but varies at each time step taking into account the thermomechanical deformations of the disc and the pad.…”

Section: Disc Brakes 3 31 Backgroundmentioning

confidence: 99%

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Finite Element Modeling of Contact Problems

Rashid¹

2016

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Contact is the principal way load is transferred to a body. The study of stresses and deformations arising due to contact interaction of solid bodies is thus of paramount importance in many engineering applications. In this work, problems involving contact interactions are investigated using finite element modeling. In the first part, a new augmented Lagrangian multiplier method is implemented for the finite element solution of contact problems. In this method, a stabilizing term is added to avoid the instability associated with overconstraining the non-penetration condition. Numerical examples are presented to show the influence of stabilization term. Furthermore, dependence of error on different parameters is investigated. In the second part, a disc brake is investigated by modeling the disc in an Eulerian framework which requires significantly lower computational time than the more common Lagrangian framework. Thermal stresses in the brake disc are simulated for a single braking operation as well as for repeated braking. The results predict the presence of residual tensile stresses in the circumferential direction which may cause initiation of radial cracks on the disc surface after a few braking cycles. It is also shown that convex bending of the pad is the major cause of the contact pressure concentration in middle of the pad which results in the appearance of a hot band on the disc surface. A multi-objective optimization study is also performed, where the mass of the back plate, the brake energy and the maximum temperature generated on the disc surface during hard braking are optimized. The results indicate that a brake pad with lowest possible stiffness will result in an optimized solution with regards to all three objectives. Finally, an overview of disc brakes and related phenomena is presented in a literature review. In the third part, a lower limb donned in a prosthetic socket is investigated. The contact problem is solved between the socket and the limb while taking friction into consideration to determine the contact pressure and resultant internal stress-strain in the soft tissues. Internal mechanical conditions and interface stresses for three different socket designs are compared. Skin, fat, fascia, muscles, large blood vessels and bones are represented separately, which is novel in this work

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Section: Disc Brakes 3 31 Backgroundmentioning

confidence: 99%

“…The frictional heat analysis, based on the Eulerian method, is performed in an in-house software developed by Strömberg, which is described in his earlier works [25,26]. The Eulerian approach gives rise to a convective velocity term in the equation of motion.…”

Section: Disc Brakes 3 31 Backgroundmentioning

confidence: 99%

Finite Element Modeling of Contact Problems

Rashid¹

2016

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“…In addition, we are using a line-search of Armijo type, which we have adopted several times for solving nonsmooth and non-linear problems in mechanics. For instance, in Strömberg (2011), it was utilized to simulate frictional heat bands in a brake disc. In Klarbring and Strömberg (2013), the state problem of hyperelastic bodies was established with this approach in order to perform topology optimization of non-linear elastic structures.…”

Section: Pr[h(y ) < 0] ≈ (−β Hl )mentioning

confidence: 99%

Reliability-based design optimization using SORM and SQP

Strömberg

2017

Struct Multidisc Optim

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In this work a second order approach for reliabilitybased design optimization (RBDO) with mixtures of uncorrelated non-Gaussian variables is derived by applying second order reliability methods (SORM) and sequential quadratic programming (SQP). The derivation is performed by introducing intermediate variables defined by the incremental iso-probabilistic transformation at the most probable point (MPP). By using these variables in the Taylor expansions of the constraints, a corresponding general first order reliability method (FORM) based quadratic programming (QP) problem is formulated and solved in the standard normal space. The MPP is found in the physical space in the metric of Hasofer-Lind by using a Newton algorithm, where the efficiency of the Newton method is obtained by introducing an inexact Jacobian and a line-search of Armijo type. The FORM-based SQP approach is then corrected by applying four SORM approaches: Breitung, Hohenbichler, Tvedt and a recent suggested formula. The proposed SORMbased SQP approach for RBDO is accurate, efficient and robust. This is demonstrated by solving several established benchmarks, with values on the target of reliability that are considerable higher than what is commonly used, for mixtures of five different distributions (normal, lognormal, Gumbel, gamma and Weibull). Established benchmarks are also generalized in order to study problems with large number of variables and several constraints. shown that the proposed approach efficiently solves a problem with 300 variables and 240 constraints within less than 20 CPU minutes on a laptop. Finally, a most well-know deterministic benchmark of a welded beam is treated as a RBDO problem using the proposed SORM-based SQP approach.

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“…Then, the heat transfer problem is solved for the corresponding frictional power. In another paper [11] this approach was implemented for simulating frictional heating in disc-pad systems.…”

Section: Introductionmentioning

confidence: 99%

“…This approach requires signicantly lower computational resources so it becomes feasible to simulate multiple brake applications. First a toolbox developed by Ström-berg, which is based and described in his earlier work [11], is used to perform the frictional heat analysis. In this Eulerian approach the contact pressure is not constant, but varies at each time step taking into account the thermomechanical deformations of the disc and the pad.…”

Section: Introductionmentioning

confidence: 99%

Sequential simulation of thermal stresses in disc brakes for repeated braking

Rashid

Strömberg

2013

Proceedings of the Institution of Mechanical Engineers, Part J:

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In this paper an ecient sequential approach for simulating thermal stresses in brake discs for repeated braking is presented. First a frictional heat analysis is performed by using an Eulerian formulation of the disc. Then, by using the temperature history from the rst step of the sequence, a plasticity analysis with temperature dependent material data is performed in order to determine the corresponding thermal stresses. Three-dimensional geometries of a disc and a pad to a heavy truck are considered in the numerical simulations. The contact forces are computed at each time step taking the thermal deformations of the disc and pad into account. In such manner the frictional heat power distribution will also be updated in each time step, which in turn will inuence the development of heat bands. The plasticity model is taken to be the von Mises yield criterion with linear kinematic hardening, where both the hardening and the yield limit are temperature dependent. The results show that during hard braking high compressive stresses are generated on the disc surface in the circumferential direction which cause yielding. But when the disc cools down, these compressive stresses transform to tensile residual stresses. For repeated hard braking when this kind of stress history is repeated, we also show that stress cycles with high amplitudes are developed which might generate low cycle fatigue cracks after a few braking cycles.

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An Eulerian approach for simulating frictional heating in disc-pad systems

Cited by 16 publications

References 24 publications

Finite Element Modeling of Contact Problems

Finite Element Modeling of Contact Problems

Reliability-based design optimization using SORM and SQP

Sequential simulation of thermal stresses in disc brakes for repeated braking

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