Impending government fuel economy standards are causing automobile manufacturers to consider innovative ways to increase the average fuel economy of their fleets. In many cases, as discussed in this study, automakers are required to push their engine operating conditions to levels not previously considered. One constraint which limits the engines to operate efficiently and salable in these conditions is torsional vibrations. Centrifugal Pendulum Vibrations Absorbers (CPVAs) are devices used to reduce the levels of these undesirable torsional vibrations without decreasing performance.In this study, we consider nonlinear interactions in systems of order-tuned torsional vi- bration absorbers with sets of absorbers tuned to different orders. In all current applications, absorber systems are designed to reduce torsional vibrations at a single order; however, when two or more excitation orders are present and absorbers are introduced to address different orders, nonlinear interactions become possible under certain resonance conditions. Under these conditions, a common example of this phenomenon occurs for orders n and 2n where crosstalk between the absorbers, acting through the rotor inertia, can result in instabilities that are detrimental to system response. In order to design absorber systems that avoid these interactions and to explore possible improved performance with sets of absorbers tuned to different orders, we develop predictive models that allow one to examine the effects of absorber mass distribution and tuning. These models are based on perturbation methods applied to the system equations of motion ultimately yielding system response features asa function of parameters of interest, notably absorber and rotor response amplitudes and stability. The model-based analytical results are compared with numerical simulations of the complete nonlinear equations of motion and are shown to be in good agreement. In addition, experimental absorbers at multiple orders were designed and tested on a controlled spin rig. The experimental data is found to be in good agreement with the analytical predictions, thus verifying the numerical and analytical studies. These results are useful for the selection of absorber parameters to achieve desired performance. For example, they allow for approximate closed form expressions for the ratio of absorber masses at the two orders that yield optimal performance. It is also found that utilizing multiple order absorber systems can be beneficial for system stability, even when only forcing at one order.In a related study, we develop relatively simple predictive formulations describing the absorber and rotor dynamics. We do this by assuming specific forms about the absorber response in order to simplify the steady state analysis of absorber systems. Utilizing these assumptions, along with physically relevant scalings, the harmonics in the system can be balanced and thus yield these predictive closed form expressions. Although unable to capture all of the subtle system instabilities, these expressions are found to accurately capture both the steady-state absorber response as well as the harmonically rich rotor response for a wide range of absorber configurations, as confirmed by both numerical and experimental data. This analysis provides accurate and simple descriptions of the system dynamics. These descriptions are useful for selection of important system parameters when designing such systems and are generalized to account for single or multiple order absorber systems.
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