This study examines a low frequency, friction induced brake vibration problem (often known as the judder phenomenon in automobiles) that is excited by the surface distortions in the rotor. A nonlinear brake system is analyzed using experimental, analytical, and numerical approaches, though the main goal is to find new or improved analytical solutions for the speed-dependent characteristics of the governing system. Initially, a two degree of freedom torsional model of the brake system with clearance nonlinearity is proposed, where the main excitation is the multiple order frictional torque, as related to the rotor profile imperfections. The nonlinear model is first simplified as a quasi-linear model by ignoring the clearance, and closed form solutions (for a decelerating system) are obtained with and without the viscous damping element. New solutions match well with the numerical integration and numerical convolution results. The nonlinear model is then numerically solved using two different methods to calculate the speed-dependent friction induced torques. The discontinuous curves are first approximated with smoothening functions, and then event detection and location algorithms are utilized. Both approaches compare well unless the discontinuous functions are poorly smoothed.
Second, quasi-linear and nonlinear models are utilized to calculate the envelopes of the response amplitudes over a range of applicable speeds. The envelope functions are first derived from the closed form analytical solutions of the quasi-linear model. In addition, a Hilbert transform based envelope curve prediction method is proposed and applied to both quasi-linear and nonlinear models. Envelope curves are calculated for single and multiple order rotor surface excitations, and the estimations match well with analytical and numerical solutions. Furthermore, the multi-term harmonic balance method is successfully adapted to construct the order domain solutions for the nonlinear model. The arc-length continuation scheme is successfully implemented and the stability of the solutions is checked.
Third, a new dynamic friction experiment is designed and constructed with a torsional resonance and clearance nonlinearity. Experimental data clearly show the speed-dependent behavior of the friction induced torque in the shaft, as controlled by the multiple orders of the rotor surface distortion. Key dynamic events that occur during a braking test are identified by using the time, frequency and order domain analyses. Measurements are finally used to validate the nonlinear and quasi-linear models over the applicable speed ranges. Finally, a nonlinear brake pad model is developed to investigate the torque amplitude behavior observed at the higher speeds in the dynamic friction experiment, and the effects of normal load and frictional constraints acting on the pad are studied. Nonlinear model is solved numerically for many normal load and constraint combinations, and the peak-to-peak variations in the friction force are compared. Tractable analytical solutions are obtained as well. Numerical and analytical solutions are validated with a bench experiment, where a translating brake band is used to replace the brake rotor. The trends explain the significance of the center of contact force concept.
|Commitee:||Dreyer, Jason, Kahraman, Ahmet, Selamet, Ahmet, Srinivasan, Manoj|
|School:||The Ohio State University|
|School Location:||United States -- Ohio|
|Source:||DAI-B 78/11(E), Dissertation Abstracts International|
|Keywords:||Analytical methods, Brake systems, Experimental techniques, Friction, Nonlinear dynamics, Vibration|
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