Bruce Geist

Tuning for Performance and Stability in Systems of Nearly Tautochronic Torsional Vibration Absorbers

This paper considers the dynamic response and performance characteristics of a special class of centrifugal pendulum torsional vibration absorbers. The absorbers of interest are designed by selection of the path that their center of mass follows, such that their dynamics are linear or nearly so, out to large amplitudes of motion, thereby avoiding the nonlinear-induced detuning that typically accompanies such responses. These order-tuned, tautochronic or isochronic, absorbers have been the subject of previous investigations, including analyses of the synchronous and certain nonsynchronous responses of systems comprised of a set of identical absorbers. The analysis and experiments have demonstrated that the synchronous response of such absorber systems can experience an instability that results in nonsynchronous responses in which a subset of absorbers have significantly larger amplitude than the corresponding synchronous response. In this study, we present results that generalize these stability results to include absorbers whose dynamics differ slightly from tautochronic by varying the absorber path such that both linear and nonlinear perturbations of perfect tuning are included. It is shown by analysis and verified by simulations that the perfect tuning case is quite special, specifically that the instability described above occurs for tunings very close to ideal and that the synchronous response can be made stable over the entire feasible operating range by employing small levels of linear and/or nonlinear detuning. Such detuning is known to have the additional benefit of resulting in smaller absorber responses and an attendant larger operating range albeit at the expense of absorber performance in terms of attenuating rotor torsional vibrations. The main conclusion of these results is that one can select a very small amount of detuning to avoid this undesirable instability and that such detuning does not have a significant effect on absorber effectiveness. The analytical results derived also provide a quantitative means of predicting synchronous absorber response amplitudes and the associated rotor torsional vibration levels, as well as the stability properties of these responses, results are very useful for the design of absorber systems.

Analysis and design of multiple order centrifugal pendulum vibration absorbers

We consider nonlinear interactions in systems of order-tuned torsional vibration absorbers. These absorbers, which consist of centrifugally driven pendulums fitted to a rotor, are used to reduce engine-order torsional vibrations in rotating machines, including automotive engines, helicopter rotors, and light aircraft engines. 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, undesirable nonlinear interactions become possible under certain resonance conditions. Under these conditions, a common example of which occurs for orders n and 2n, 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, we develop predictive models that allow one to select proper tuning and sizing of the absorbers. These models are based on perturbation methods applied to the system equations of motion, and they yield system response features, including absorber and rotor response amplitudes and stability, as a function of parameters of interest. The model-based analytical results are compared against numerical simulations of the complete nonlinear equations of motion, and are shown to be in good agreement. These results are useful for the selection of absorber parameters for 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.Copyright

Dynamic Modeling of a Variable Displacement Vane Pump Within an Engine Oil Circuit

Automakers and the car-buying public maintain a strong and continuing interest in enhanced vehicle efficiency. Ideally, adaptively controlled oil pumps supply only enough flow within an engine to satisfy its performance requirements. Any extra flow wastes energy. In order to better understand how to improve engine and engine oil circuit efficiency, and to assess pump stability, a detailed dynamic model of a variable displacement vane pump (VDVP) is developed. This detailed pump model is mated to a simplified engine oil circuit model. This marriage allows for a detailed prediction of pump response under various simulated engine operating conditions. The VDVP modeled here adapts its pump chamber volumes according to 1) the feedback oil pressure provided from the engine oil circuit and 2) according to the sizing and installed compression loading of an internal spring. Many phenomena such as internal leakage from one pump chamber volume to another, variable oil conditions such as aeration and viscosity, as well as variations in choice for the internal spring rate and preload can be investigated for their effects on oil pump behavior and performance within the simplified oil circuit.Copyright

Accounting for roller dynamics in the design of bifilar torsional vibration absorbers

Centrifugal pendulum vibration absorbers are used for reducing torsional vibrations in rotating machines. The most common configuration of these devices utilizes a bifilar suspension in which the absorber mass rides on a pair of rollers, whose mass is small compared to that of the absorber. These rollers are typically solid steel cylinders that allow the CPVAs to move along a prescribed path relative to the rotor, determined by the shape of machined cutouts on the rotor and the absorber mass. Previous studies have considered how to account for the roller dynamics in selecting the linear tuning characteristics of the absorber system, but have not quantified the errors induced by the common approximations that either ignores their effects completely, or does not account for the nonlinear aspects of their dynamics. In this paper we systematically investigate these effects. Specifically, we first show that there exists an absorber path for which the absorber/roller system maintains the same frequency of free oscillation over all physically possible amplitudes. This tautochronic path has been well known for the case with zero roller inertia, and herein, for the first time, the corresponding path with rollers is shown to exist and is constructed. In addition, we carry out an analysis of the steady-state response of the rotor/absorber/roller system in order to quantify the effects of various approximations commonly used in regards to the roller dynamics. This analysis is based on the equations of motion, scaled in such a manner so that they are amenable to a perturbation analysis, which includes the effects of rollers in the perturbation terms. It is shown that if one accounts for the linear tuning aspects of the rollers, the system response is essentially insensitive to the selection of the nonlinear tuning parameter, so long as it is close to the tautochronic value. This implies that the approximation commonly used for selecting absorber paths with rollers is adequate.Copyright

Reduced-order thermal modeling of liquid-cooled lithium-ion battery pack for EVs and HEVs

Adequate thermal management is critical to maintain and manage lithium-ion (Li-ion) battery health and performance within Electrical Vehicles (EVs) and Hybrid Electric Vehicles (HEVs). Numerical models can assist in the design and optimization of thermal management systems for battery packs. Compared with distributed models, reduced-order models can predict results with acceptable accuracy and much lower computational cost. Therefore, to provide design insight, reduced-order models are often employed for predicting transient thermal and electrical behaviors of a battery pack. This paper presents the development, validation, and application of a detailed, reduced-order thermal model of a battery pack with liquid cooling. The model described is capable of predicting the average temperature of each individual cell. It was first developed in a general vehicle modeling software environment in which an equivalent circuit model captures the electrical characteristics of each cell. A structural-thermal model captures the heat transfer among the cells, the cooling liquid, as well as temperatures of other components inside the battery pack. Calibration and validation of the model is performed with test data that includes cell state of charge (SOC), terminal voltage, coolant temperature, and cell temperature data.

Modal Properties of Rotating Shafts with Order-Tuned Absorbers

We consider the properties of torsional vibration modes of rotating shafts fitted with centrifugally driven pendulum vibration absorbers. These systems feature interesting modal behavior that arises from the coupling of constant-stiffness elements, namely the shaft torsional modes, and engine-order-based elements, namely the absorbers. These models are relevant to automotive crankshafts fitted with pendulum absorbers, which are being considered for reducing vibrations in a number of advanced technology engines. The coupled system modes exhibit frequency veering as the rotor speed varies, and when the system is subjected to engine-order excitation the resonances depend in a non-trivial manner on the system parameters. The absorbers are typically tuned to suppress shaft torsional vibrations, and proper tuning of the absorbers requires a thorough understanding of this resonance behavior. In this paper we describe the manner in which natural frequencies depend on rotor speed and how this influences the overall frequency response of the rotor. We also discuss how to tune absorbers to achieve the desired vibration reduction, and we consider some examples that demonstrate the rich response behavior of these systems.

Analysis and Customization of Rocker Arm Joint Sliding Velocity

This paper examines how the sliding motion between a rocker arm and a valve stem tip can be adjusted by reshaping the rocker pad surface. The valve tip is assumed flat, and the rocker arm and valve stem are assumed to lie in a common plane. It is shown that the rubbing velocity between a rocker arm and a valve stem tip, as well as the curvature of the rocker arm pad, may be determined from two features of the contact: (I) the contact point path between the rocker arm and the valve stem tip and (2) the angle that the valve stem tip makes with the line connecting the rocker pivot to the zero-lift point of contact. An algorithm is presented for determining a rocker arm surface from a prescribed contact point path and valve angle. The derived technique enables customization of rocker arm pad curvature and rocker arm joint sliding velocity.