MATHEMATICAL MODELLING AND AN EXPERIMENTAL STUDY FOR VEHICLE BRAKING FORCE ANALYSIS

Yıl 2005, Cilt: 18 Sayı: 3, 489 - 503, 12.08.2010

Hüseyin Bayrakçeken , Duran Altınparmak

Öz

ABSTRACT

Braking performance is an important criteria for the vehicle safety and for the conditions of brake system elements. Many factors such as the wheel-road interaction and elements of brake system condition affect the brake performance. However these factors can be measured by brake test equipment, brake forces for a vehicle can also be analyzed by using mathematical models. In this experimental study, brake force analysis has been done by measuring the changes of brake forces and by using a mathematical model based on the obtained experimental data. For this purpose, hydraulic brake test equipment has been developed by using electronic equipment and a data acquisition system. By using the developed equipment, a mathematical formulation is obtained by considering the effective factors of brake force i.e, the tire thread depth, the variation of road conditions, tire air pressure etc. There is a good agreement between the experimental data and the developed mathematical model. The change of braking force with respect to the ratio of sliding was calculated; when one parameter was changing, the others was kept constant in this calculation and this was done using 3 kN vertical force. The statistical coefficient of multiple determinations (R2 value) varied between 0.967 and 1.0.

Anahtar Kelimeler

Key Words: Mathematical model, Brake Force, Brake

TAŞITLARDA FRENLEME KUVVETİ ANALİZİ İÇİN MATEMATİK MODELLEME VE DENEYSEL BİR ÇALIŞMA

Öz

Taşıtlarda frenleme performansı, fren sisteminin durumunu ortaya koyması bakımından oldukça önemlidir. Frenleme performansını, fren sistem elemanları ve tekerlek–yol şartları gibi faktörler doğrudan etkilemektedir. Bu faktörlerin fren kuvvetleri üzerindeki etkileri, deneysel yöntemlerle tespit edilebileceği gibi matematiksel modeller yoluyla kestirilmesi mümkündür

Anahtar Kelimeler

Matematiksel model, Fren kuvveti, Fren

Kaynakça

• 1. Limpert. R., Brake Design and Safety, Second Edition, Society of Automotive Engineers Inc. United States of America, 1999
• 2. Jagt. P.V.D., Parson. A.W., Road Surface Correction Of Tire Force And Moment Data, Tyre Models for Vehicle Dynamics Analysis, Edited by H.B. Pacejka, Proceeding 1.st International Colloquium on Tyre Models For Vehicle Dynamics Analysis, Netherland, 1991
• 3. Segel. L., An Overview Of Developments in Road-Vehicle Dynamics, Past, Present and Future, Proceedings of the Institution of Mechanical Engineers, Vehicle Ride and Handling International Conference, 1993
• 4. Holmes. K.E., Stone. R.D., Tyre Forces as Functions of Cornering And Braking Slip on Wet Road Surfaces,, Road Research Laboratory Ministry of Transport RRL Report Lr 254, Crowthorne, Berkshine,1-43, 1969
• 5. Lıu. C.S., Peng. H., Road Friction Coefficient Estimation for Vehicle Path Prediction, Vehicle System Dynamics, vol. 25, 413-425, 1996
• 6. Gindy. M.E., Ilosvai. L., Vehicle Stability During Braking Manoeuvres, Int.J. of Vehicle Design. vol.1, No.3, England, 1980
• 7. Oppenheimer, P., Comparing Stopping Capability of Cars with and Without Antilock Braking System (ABS), SAE Paper No: 880324, 1988
• 8. Maalej. A.Y., Guenther. D.A., Ellis. J.R., Experimental Development of Tyre Force and Moment Models, Int. J. of Vehicle Design. Vol. 10, No. 1, 34-50, 1989
• 9. Lugner.P., Mittermayr.P., A Measurement Based Tyre Characteristics Approximation, Tyre Models for Vehicle Dynamics Analysis, Edited by H.B. Pacejka, Proceeding 1.st International Colloquium on Tyre Models For Vehicle Dynamics Analysis, Nether land, 1991
• 10. Pacejka. H.B., Takahashi. T., Pure Slip Characteristics of Tyres on Flat and on Undulated Road Surfaces”, SAE Paper No:923064, Proc. Int. Symp. Advanced Vehicle Control, Japan, 1992
• 11. Pacejka. H.B., Sharp. R.S., Shear Force Development by pneumatic Tyres in Steady State Conditions: A Review of Modelling Aspects, Vehicle System Dynamics, 20, 121-176, 1991
• 12. Shang.L.C., Peng.H.,”Road Friction Coefficient Estimation For Vehicle Path Prediction”, Vehicle System Dynamics, Vol 25, pp.413-425, 1996
• 13. Lacombe.J., “Tire Model For Simulations Of Vehicle Motion On High And Low Friction Road Surfaces”, Proceeding of the 2000 winter simulation conference, pp.1025-1034, 2000, U.S.A.
• 14. Bayrakçeken, H., “Motorlu Taşıtlarda Fren Performans Analizi Ve Geliştirilen Test Cihazında Uygulaması”, Doktora Tezi, Gazi Üni. Fen Bil. Ens. Ankara, 2002
• 15. Pacejka, H.B., Bakker, E., Takahashi, T., Description of Tyre Behaviour Including Side Slipping on Uneven Roads, Vehicle. System. Dynamics, 1-14, 1987
• 16. Clark S.K. Mechanics of Pneumatic tires”, DOT HS-805 952, 1981
• 17. Taheri S., Law. E. H., Slip Control Braking of an Automobile During Combined Braking And Steering Manoeuvres, Advanced Automotive Technologies, ASME, vol 40, 1991
• 18. Bernard. J.E., Segel. L., Wild. R.E., Tire Shear Force Generation During Combined Steering and Braking Manoeuvres, SAE Paper No: 770852, 1977
• 19. Stewart. E.E., Bowler. L.L., Road Testing of Wheel Slip Control Systems in the Laboratory, International Automotive Engineering Congress, Detroit, Mich, SAE paper, No:690215, 1969