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Technical Paper

Critical Speed Vibrations Induced by Unstable Gyroscopic Moment

Critical speed induced by imbalance forces is a well-known dynamic behavior of rotating shafts. Such problems are typically found in flexible shafts or rigid shafts with flexible supports when the frequency of rotation reaches the natural frequencies of the shaft. This simple critical speed problem is well understood and formulated in many engineering texts. However, not all critical speed phenomena are induced by imbalance. A perfectly balanced shaft with certain inertial properties also reaches a critical speed condition at a rotational speed that is not equal to the natural frequency of the shaft. Several variables of the dynamic system play a role on the critical speed condition, which is mainly induced by the unstable gyroscopic moment acting on the shaft. The unstable gyroscopic moment forces the shaft bearings to deflect causing precession about the undeflected geometric centerline of the shaft, but the rotation and precession speeds remain synchronized at low speeds.
Technical Paper

Dynamic Properties of Styrene-Butadiene Rubber for Automotive Applications

Styrene-Butadiene Rubber (SBR) is a copolymer of butadiene and styrene. It has a wide range of applications in the automotive industry due to its high durability, resistance to abrasion, oils and oxidation. SBR applications vary from tires to vibration isolators and gaskets. SBR is also used in tuned dampers which aim to reduce and control the angular vibrations of crankshafts, acting as an isolator and energy absorber between the tune damper's hub and the inertia ring. The dynamic properties of this polymer are therefore, very important in developing an appropriate analytical model. This paper presents the results of a series of experiments performed to determine the dynamic stiffness and damping properties of SBR. The frequency, temperature and displacement dependent properties are determined in a low frequency range from 0.4 to 150 Hz, and in a mid frequency range from 150 to 550 Hz. The most interesting property of SBR is its frequency dependent behavior.
Technical Paper

Computing Transfer Functions from Mass Loaded Response of Structures

This paper outlines a method for computing the transfer functions of structures using their mass loaded responses. According to the method, scaled transfer functions are computed from the response of a structure and without any knowledge of the input forces. The paper outlines the analytical approach, develops the necessary equations for the computation of transfer functions between a mass loading point and other points on a linear dynamic system. A numerical example to show the validity, advantages and limitations of the method is also provided. Currently, the method can be applied to the responses obtained from analytical simulations where it may be necessary to compute coupled response of a simulated dynamic system with other dynamic systems that are not (or cannot be) included in a simulation. It is not uncommon that many dynamic simulations exclude certain coupling effects between the main and the auxiliary systems.
Technical Paper

Computing The Optimum Knock Sensor Locations

This paper describes a computational technique and a procedure to select the optimum knock sensor locations in order to augment the currently employed measurement techniques. The technique is Finite Elements based and uses the Frequency Domain Forced Response Analysis to estimate the vibration propagation on an engine block. The results are post processed to obtain the RMS value of normal surface vibrations. The optimum location for the knock sensor is then obtained from the RMS value contributions of potential knock pressures from each cylinder. The predictive ability of the method has been tested against actual measurement data during several development programs where a good agreement with the sensor locations determined by measurements and the computational method was obtained. The method can be instrumental in indicating optimal measurement locations and potentially reduce the amount of data collected.
Technical Paper

Modeling the Stiffness and Damping Properties of Styrene-Butadiene Rubber

Styrene-Butadiene Rubber (SBR), a copolymer of butadiene and styrene, is widely used in the automotive industry due to its high durability and resistance to abrasion, oils and oxidation. Some of the common applications include tires, vibration isolators, and gaskets, among others. This paper characterizes the dynamic behavior of SBR and discusses the suitability of a visco-elastic model of elastomers, known as the Kelvin model, from a mathematical and physical point of view. An optimization algorithm is used to estimate the parameters of the Kelvin model. The resulting model was shown to produce reasonable approximations of measured dynamic stiffness. The model was also used to calculate the self heating of the elastomer due to energy dissipation by the viscous damping components in the model. Developing such a predictive capability is essential in understanding the dynamic behavior of elastomers considering that their dynamic stiffness can in general depend on temperature.