This paper presents the nonlinear frequency response of a multistage clutch damper system in the framework of the harmonic balance method. For the numerical analysis, a multistage clutch damper with multiple nonlinearities is modeled as a single degree-of-freedom torsional system subjected to sinusoidal excitations. The nonlinearities include piecewise-linear stiffness, hysteresis, and preload all with asymmetric transition angles. Then, the nonlinear frequency response of the system is numerically obtained by applying the Newton–Raphson method to a system equation formulated by using the harmonic balance method. The resulting nonlinear frequency response is then compared with that obtained by direct numerical simulation of the system in the time domain. Using the simulation results, the stability characteristics and existence of quasi-harmonic response of the system are investigated. Also, the effect of stiffness values on the dynamic performance of the system is examined.

The scope of this article is limited to the torsional driveline system of a front-engine front-wheel type of vehicle. A reduced-order model of a manual transmission (with the third gear engaged and the fifth gear unloaded) is developed on the basis of the modal characteristics. A simplified nonlinear mathematical model is then proposed with the focus on the multi-staged clutch damper properties such as the asymmetric transition angles and the pre-loads. The drag torque is estimated under two engine conditions (wide-open throttle and coast) by assuming that the vehicle is in the steady-state condition. Finally, the gear rattle criteria are investigated, and illustrative examples for three real-life clutch dampers are described. In particular, methods for solving the real-life gear rattle phenomenon are suggested.

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Torsional systems with clearance-type nonlinearities have inherent vibratory problems such as gear rattle. Such vibro-impacts generally occur on the unloaded gear pairs of a vehicle correlated with the firing excitation of an engine. This study investigates the gear rattle phenomena on unloaded gear pairs with different excitation conditions and various system parameters. First, a linear time-invariant system model with six degrees of freedom is constructed and then a numerical analysis is applied to the gear rattle motion. Smoothening factors for clutch stiffness and hysteresis are employed for the stability of numerical simulations. Second, the dynamic characteristics of vibro-impacts are studied by examining the fast Fourier transform (FFT) components of the gear mesh force in a high frequency range. The effects of various system parameters on the vibro-impacts are examined using a nonlinear system model. Finally, the vibro-impacts, in terms of “single-sided” and “double-sided” impacts, are identified in phase planes.

Calibration of an energy simulation with actual data has generally been considered too difficult to be part of the energy audit procedure. The purpose of this paper is to develop a systematic method using a “base load analysis approach” to calibrate a building energy performance model with a combination of monthly utility billing data and sub-metered data such as is commonly available in large buildings in Korea. The calibration procedure was specifically developed to be suitable for use in both the audit and savings determination procedure within a retrofit process. The procedure has been visualized using a logical flow chart and demonstrated using the simulation of a 26-story commercial building located in Seoul as a case study. The results indicate that the approach developed provided a reliable and accurate simulation of the monthly and annual building energy requirements of the case study building.

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