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Simulation of Thermal Stresses in a Brake Disc
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis thermal stresses in a brake disc during a braking operation are simulated. The simulations are performed by using a sequential approach where the temperature history generated during a frictional heat analysis is used as an input for the stress analysis. The frictional heat analysis is based on the Eulerian method, which requires signicantly lower computational time as compared to the Lagrangian approach. The stress analysis is performed using a temperature dependent material model both with isotropic and kinematic hardening behaviors. The results predict the presence of residual tensile stresses in circumferential direction for both hardening behaviors. These residual stresses may cause initiation of radial cracks on the disc surface after a few braking cycles. For repeated braking an approximately stable stress-strain loop is obtained already after the rst cycle for the linear kinematic hardening model. So, if the fatigue life data for the disc material is known, its fatigue life can be assessed. These results are in agreement with experimental observations available in the literature.

The simulation results predict one hot band in the middle of the disc for a pad with no wear history. 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. The results also show that due to wear of the pad, dierent distributions of temperature on the disc surface are obtained for each new brake cycle and after a few braking cycles, two hot bands appear on the disc surface.

This sequential approach has proved tremendously cheap in terms of computational time so it gives the freedom to perform multi-objective  optimization studies. Preliminary results of such a study are also presented 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 stiness will result in an optimized solution with regards to all three objectives. Another interesting result is the trend of decrease in maximum temperature with an increase in back plate thickness.

Finally an overview of disc brakes and related phenomena is presented as a literature review.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. , 23 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1603
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-94345Local ID: LIU-TEK-LIC-2013:37ISBN: 978-91-7519-575-9 (print)OAI: oai:DiVA.org:liu-94345DiVA: diva2:632213
Presentation
2013-08-29, Sal A33, A-huset, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Opponent
Supervisors
Available from: 2013-06-24 Created: 2013-06-24 Last updated: 2013-06-25Bibliographically approved
List of papers
1. An Efficient Sequential Approach for Simulation of Thermal Stresses in Disc Brakes
Open this publication in new window or tab >>An Efficient Sequential Approach for Simulation of Thermal Stresses in Disc Brakes
2012 (English)Conference paper, Published paper (Other academic)
Abstract [en]

In this paper an ecient approach to simulate thermal stresses due to tem-perature variations in disc brakes is presented. In the approach thermal and stress analysis are performed sequentially. The frictional heat analysis is based on the Eulerian method, which requires signicantly low computational time as compared to the Lagrangian approach. The nodal temperature history is recorded at each time step and is used in a sequentially coupled stress analysis, where a temperature dependent elasto-plastic material model is used to compute the stresses in the disc brake. The results show that during hard braking, high compressive stresses are generated on the disc surface in circumferential direction which cause plastic yielding. But when the disc cools down, the compressive stresses transform to tensile stresses. Such thermoplastic stress history may cause cracks on disc surface after a few braking cycles. These results are in agreement with experimental observations available in the literature.

National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-94281 (URN)
Conference
15th Nordic Symposium on Trbology, NORDTRIB,Trondheim, Norway, 12-15 June
Available from: 2012-09-17 Created: 2013-06-20 Last updated: 2016-02-16Bibliographically approved
2. Sequential simulation of thermal stresses in disc brakes for repeated braking
Open this publication in new window or tab >>Sequential simulation of thermal stresses in disc brakes for repeated braking
2013 (English)In: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 227, no 8, 919-929 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, an efficient 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 first 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 influence 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.

Place, publisher, year, edition, pages
Sage Publications, 2013
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-94283 (URN)10.1177/1350650113481701 (DOI)
Available from: 2013-04-26 Created: 2013-06-20 Last updated: 2017-12-06Bibliographically approved
3. Thermomechanical Simulation of Wear and Hot Bands in a Disc Brake by adopting an Eulerian approach
Open this publication in new window or tab >>Thermomechanical Simulation of Wear and Hot Bands in a Disc Brake by adopting an Eulerian approach
2013 (English)In: EuroBrake 2013 Conference Proceedings, FISITA , 2013Conference paper, Published paper (Other academic)
Abstract [en]

In this paper frictional heating of a disc brake is simulated while taking wear into account. By performing thermomechanical finite element analysis, it is studied how the wear history will influence the development of hot bands. The frictional heat analysis is based on an Eulerian formulation of the disc, which requires significantly lower computational time as compared to a standard Lagrangian approach. A real disc-pad system to a heavy truck is considered, where complete three-dimensional geometries of the ventilated disc and pad are used in the simulations. A sequential approach is adopted, where the contact forces are computed at each time step taking the wear and thermal deformations of the mating parts into account. After each brake cycle, the wear profile of the pad is updated and used in subsequent analysis. The results show that when wear is considered, different distributions of the temperature on disc are obtained for each new brake cycle. After a few braking cycles two hot bands appear on the disc surface instead of only one. These results are in agreement with experimental observations.

Place, publisher, year, edition, pages
FISITA, 2013
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-94284 (URN)978-0-9572076-0-8 (ISBN)
Conference
EuroBrake 2013, Chassis Brakes International, Dresden, Germany, June 17-19, 2013
Available from: 2013-06-20 Created: 2013-06-20 Last updated: 2016-03-07Bibliographically approved
4. Multi-Objective Optimization of a Disc Brake System by using SPEA2 and RBFN
Open this publication in new window or tab >>Multi-Objective Optimization of a Disc Brake System by using SPEA2 and RBFN
2013 (English)Conference paper, Published paper (Other academic)
Abstract [en]

Many engineering design optimization problems involve multiple conflicting objectives, which today often are obtained by computational expensive finite element simulations. Evolutionary multi-objective optimization (EMO) methods based on surrogate modeling is one approach of solving this class of problems. In this paper, multi-objective optimization of a disc brake system to a heavy truck by using EMO and radial basis function networks (RBFN) is presented. Three conflicting objectives are considered. These are: 1) minimizing the maximum temperature of the disc brake, 2) maximizing the brake energy of the system and 3) minimizing the mass of the back plate of the brake pad. An iterative Latin hypercube sampling method is used to construct the design of experiments (DoE) for the design variables. Next, thermo-mechanical finite element analysis of the disc brake, including frictional heating between the pad and the disc, is performed in order to determine the values of the first two objectives for the DoE. Surrogate models for the maximum temperature and the brake energy are created using RBFN with polynomial biases. Different radial basis functions are compared using statistical errors and cross validation errors (PRESS) to evaluate the accuracy of the surrogate models and to select the most accurate radial basis function. The multi-objective optimization problem is then solved by employing EMO using the strength Pareto evolutionary algorithm (SPEA2). Finally, the Pareto fronts generated by the proposed methodology are presented and discussed.

Place, publisher, year, edition, pages
The American Society of Mechanical Engineers, 2013
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-94285 (URN)10.1115/DETC2013-12809 (DOI)978-0-7918-5590-4 (ISBN)
Conference
ASME 2013 International Design Engineering Technical Conferences (IDETC) and Computers and Information in Engineering Conference (CIE), Portland, USA, August 4-7, 2013
Note

Paper No. DETC2013-12809, pp. V03BT03A029; 10 pages.

Available from: 2013-06-20 Created: 2013-06-20 Last updated: 2016-02-04Bibliographically approved
5. Overview of Disc Brakes and Related Phenomena - a literature review
Open this publication in new window or tab >>Overview of Disc Brakes and Related Phenomena - a literature review
2013 (English)Report (Other academic)
Abstract [en]

Disc brakes have evolved over time to be a reliable method of decelerating and stopping a vehicle. There have been dierent designs of disc brake systems for dierent applications. This review gives a detailed description of dierent geometries of the components and the materials used in a disc brake system. In spite of all the improvements, there are still many issues related to disc brakes that need to be understood in a greater detail and resolved. There has been a lot of research going on about these issues and at the same time dierent methods are being proposed to eliminate or reduce them. These methods include the changes in geometry of dierent components, dierent or improved materials, addition of new components and changes in cooling methods etc. There has also been an intensive research going on about the evolution of tribological interface of disc-pad system. One major purpose of the present paper is to give a comprehensive overview of all such developments.

Publisher
45 p.
Series
JTH research report, ISSN 1404-0018
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:liu:diva-94282 (URN)
Available from: 2013-04-18 Created: 2013-06-20 Last updated: 2013-06-24Bibliographically approved

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