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4.DISCUSSONS AND FUTURE WORK
The one-dimensional system model for drag problem is developed based on the dynamic system represented by Eq. (1). It includes the major parameters that affect the drag performance of a caliper brake system. It has been demonstrated that the simulation model correctly captures the essence of the caliper drag problem and provides an effective avenue to guide the caliper brake designs. However, drag is a complicated problem that requires accurate characteristics, such as dynamic response of seal/groove, hysteresis and dynamic behaviors of lining material, and stick-slide behavior deserves more thorough studies. Operating temperature, which is not included in this study, can significantly affect the rubber seal behavior and lining properties, and consequently the drag performance. The subsequent study will address these issues to reline the model and improve the accuracy of the simulation.
The model can also be expanded to more general caliper brake problems by taking into account of the interaction between the two directions, Eq. (1) and Eq.(2). Figure 13 shows some preliminary results of such a model for predicting on-brake and off-brake responses of a caliper system. Figure 13(a) shows the brake torque variation during a brake apply, release, and off-brake process. The rotor has a small amount of first order lateral runout. Due to the nature of a "floating" caliper, the braking torque does not show a significant oscillation. However, the presence of the drag torque after braking is clearly seen in the plot. Figure 13(b) shows a similar plot for a system with a rotor that has a first order disc thickness variation. In this case, the oscillation in the brake torque is very significant, indicating a brake pulsation may be felt by the driver. During the off-brake, the drag torque also exhibits an oscillating behavior. More results will be released in due time.
5.CONCLUSIONS
It is demonstrated that the simulation results of a simplified one-dimensional dynamic system model developed herein correlate reasonably with the experimental data on both fluid displacement and drag performance. The predicted "residual retraction" is correlated with drag performance and thus used in the study as a drag performance index. The parameter study and case study using this model not only explore the general trend of the drag performance resulting from the interaction among design parameters, but also demonstrate the merit of this simplified system approach for brake engineers to perform trade-off studies among the design parameters. The simulation model grants the brake engineers more freedom and control in the design of the caliper system at the early stage of product development. In addition, the predictive capabilities of this model has demonstrated its effectiveness to quickly and thoroughly evaluate a disc brake design and help brake engineers to achieve an optimal brake performance. With this tool, engineers can reduce their reliance on engineering intuition and prototype experiments. Both product development lead-time and prototype cost may be saved. Finally, with the capability of predicting the interactive impact to the residual drag torque performance, the model can also be extended to simulate other field related performance concerns in a disc brake system, such as pedal feel and drag torque variation with lateral rotor runout and rotor thickness variation.
ACKNOWLEDGMENT
The authors are grateful to Dr. Jin-Jae Chen, for his involvement with their initial study and valuable recommendations to the model development.
REFERENCES
1. Okon D. Anwana, Hao Cai , and H. T. Chang, Analysis of Brake Caliper Seal-Groove Design, SAE 2002 World Congress, SEA 2002-01-0927.
2. Hao Cai and Okon Anwana, Seal/GroovePerformance Analysis Models, 20 th Annual Brake Colloquium and Exhibition , SAE 2002-01-2588