| Vibration and noise from disk brakes negatively affect passenger comfort and perceptions of quality in both the automotive and aircraft industries. With regulatory pressure for stopping distance and the emphasis on smaller and lighter components, new brakes not only have to meet design and performance requirements, but must minimize vibration as well. Although materials and geometries vary from application to application, disk brakes generally consist of rotating annular disk(s) subjected to in-plane friction which dissipates the kinetic energy of the vehicle. During this process, friction-induced vibration of the disk(s) occurs, resulting in brake noise. Although sound radiation results from a disk's out-of-plane vibration, substantial in-plane motions must also be present due to the in-plane friction. This in-plane vibration can play a key role in the dynamics of the friction interface and hence, in brake noise and vibration.; In this thesis, experimental and analytical methods are used to study the in-plane vibration of annular disks with a view toward understanding disk brake vibration. The issues that are addressed and the major findings include: (1) Characterization of in-plane modes in annular disks. For automotive rotors and thick annular disks, in-plane modes of vibration have frequencies that are both comparable to low-order bending modes and within the measured range for brake squeal. Despite the large in-plane friction force provided by disk brakes, no existing model includes in-plane disk motion with in-plane friction. A three-dimensional vibration model is used to determine frequencies and mode shapes for an annular disk subject to two boundary conditions: all surfaces traction-free, and all free except for a constrained inner edge. (2) Identification of frequency clusters. Using experimental and analytical methods, the frequencies for families of in-plane modes are found to converge to a common value with increasing disk thickness to the limit of the disk becoming a long “cylinder.” Consequently, these modes have frequencies that are indistinguishable at a given experimental or numerical resolution, despite having different numbers of axial nodes. The steady-state harmonic response at frequencies near the cluster can have spatially confined displacements which decay rapidly away from the point of maximum response. (3) Simulation of braking events. The vibration of an automotive disk brake is modeled by a thick annular disk subjected to in-plane friction distributed over a sector of the disk's two faces. The response of the disk is obtained through modal analysis where three-dimensional mode shapes are used to discretize the forced response. In transient simulations of a braking event, the response of the disk can be characterized by three distinct phases: growth, linear decay and final decay. These phases originate from friction's role as an exciting mechanism, a dissipating mechanism, or both. |
