G. William Fan

Bio: G. William Fan is an academic researcher. The author has contributed to research in topics: Modal analysis & Pulley. The author has an hindex of 1, co-authored 1 publications receiving 3 citations.

Complex Modal Analysis of a Flat Belt Pulley System With Belt Damping and Coulomb Damped Tensioner

Abstract: The effects of damping on rotational vibratory solutions of a multiple pulley-flat viscoelastomeric belt system with rotary arm tensioner is developed. A complex model procedure is developed to solve both underdamped and overdamped cases. This complex modal procedure allows for future extension to include nonsymmetric rotational models, such as transverse belt vibration coupling. The modal solution enables rapid analysis over a spectrum of frequencies. Seven pulley system experimental results reported in the literature support the analytical development. Belt damping has significant vibration and belt tension amplitude effects. Tensioner spring rate and coulomb damping has minor effects.

Modeling and optimization of power losses in poly-V belt transmissions : Application to the Front Engine Accessory Drive of trucks

Abstract: This work is a part of the Efficient Distribution Truck (EDIT, FUI 19) project, led by Volvo Trucks, whose objective is to reduce distribution vehicles’ fuel consumption for 2020 by 13% when compared with the current production vehicle EURO-6. The EDIT project targets five areas of research and technical solutions, one of which consists of obtaining an optimized poly-V belt transmission concerning the power losses. In terms of lifetime of the mechanical components, reduction of noise and vibrations, the Front Engine Accessory Drives (FEADs) are currently one of the most technologically sophisticated systems. However, further improvements can be made to make the vehicles more energy efficient. This thesis, which aims at investigating possibilities for reducing and optimizing the power losses in the FEADs, is composed of three main parts: the characterization of the viscoelastic materials of the poly-V belts via Dynamic Mechanical Analysis (DMA) and the FEAD components; the modeling, the optimization and the implementation of the power loss models in a simulation tool; and their experimental validation through a test bench. The power losses occurring in a FEAD are of several types: poly-V internal losses (hysteresis of the belt-rubber), poly-V external losses (belt/pulley slip) and losses from the accessory drives (friction inside the bearings). These power losses can be quantified and optimized thanks to the models developed throughout this thesis. These models have been validated and implemented in a simulation tool (PLFead, Power Loss Front engine accessory drive), which has been developed to optimize the power losses taking into consideration the design parameters and operating conditions of the FEAD.

Estudo de vibrações em auto-tensionador de transmissão por correias

Abstract: Neste trabalho desenvolve-se um metodo, que permite avaliacoes de parâmetros, para o estudo do projeto de um sistema auto-tensionador no controle de suas vibracoes transversais e forcas atuantes. Parâmetros construtivos e operacionais, como: a geometria, inercia, rigidez da mola do auto-tensionador, rigidez da correia e condicoes de operacao, como: frequencias de excitacao, forcas estaticas e dinâmicas sao obtidas em um sistema auto-tensionador de transmissao por correias, aplicados em automoveis de passeio comerciais. Com a modelagem dinâmica de um grau de liberdade, calcula-se a forca de atrito e fator de amortecimento, que estabelece o controle de vibracoes e forcas atuantes no sistema. Os resultados das simulacoes computacionais sao analisados e comparados com os resultados obtidos pelo prototipo experimental desenvolvido. Os resultados tecno-experimentais indicam ajuste satisfatorio, o que representa uma contribuicao significativa, para o estudo de sistemas auto-tensionadores e na melhoria do controle de vibracoes e forcas atuantes em correias dentadas, em tempo real de projeto Abstract

Effect of Shaft Vibration on the Dynamics of Gear and Belt Drives

Abstract: Gear and belt drives are widely used as effective means of tra nsmitting power including, but not limited to automobiles, heavy duty vehicles, he licopters, etc. Noise and wearrelated failures in these systems have their roots in the vib ration of different components of these systems (e.g., the dynamic forces at the gear mesh is a m ajor source of noise in a gear box). Secondary sources of noise appear due to vibration of v arious internal components such as shafts and bearings. This work aims at developing lin ear mathematical models for single-mesh spur and helical gears mounted on compliant par allel shafts, with and without considering gyroscopic effects, and single span of a ser pentine belt with pulleys also mounted on parallel compliant shafts. The findings of the res arch can provide practical guidance during design or troubleshooting under operating co ditions. Spur gears are simple to design and widely used to transmit po wer from a drive shaft to a driven shaft in many applications. In the majority of cases , the rotational speeds are low. A mathematical model for the closed form approximate eigens olution of a pair of coupled non-gyroscopic spur gears on parallel shafts is developed. The model is a hybrid discretecontinuous one where the gears modeled as rigid disks along w ith the mesh spring form the discrete elements while the elastic shafts having trans verse as well as torsional flexibility constitute the continuous elements. The non-dimens ional governing equations along with the natural boundary conditions are developed using th e Hamilton’s principle. The governing equations of the shafts for flexural and torsional vibrations and the equations of ii motion of the disks are written in an extended operator form t o prove the self-adjointness of the system. Matching boundary conditions at the disk-sha ft interfaces prevent the use of Galerkin’s method, a natural extension of the extended oper ator formulation. An efficient Rayleigh’s principle based energy method, the assumed mode s method is used to discretize the system equations where the matching conditions are inco rporated with the use of Lagrange multipliers. Orthonormal global basis functions fo r flexure and torsion are chosen from separate families. The sensitivities of the natural fr equencies of different modes to mesh stiffness, torsional and flexural rigidities of the sha fts, and lengths of the shafts are examined and the results are correlated with the modal energ y distributions. Excitation in the form of the loaded static transmission error at the gear m esh is identified and converted to the discretized form and the response for the same is calcu lated. Helical gears are employed for quiet operation in drive trai ns where the rotational speeds are sufficiently high. Three-dimensional gyroscopi c model of a pair of helical gears mounted at the ends of compliant spinning shafts is develope d. The gears are modeled as rigid disks with the tooth compliance modeled as translatio nal and rotational springs connecting the disks with the shafts having transverse and tors ional vibrations. The rotational spring at the gear mesh accounts for the energy stored due to t h relative tilting of the gears. The rotational speed is high and therefore, the gyroscopic e ffe t is non-negligible. Hamilton’s principle is used to obtain the non-dimensional gover ning equations and equations of motion of the disks. Excitation in the form of the loaded stat ic transmission error at the gear mesh is incorporated in the equations of motion. This excita tion appears as a combination of forces and moments and these are identified from the expres sion of the virtual work. An extended operator formulation is employed to simplify the s ystem equations to a compact analytical form, which is prototypical of a gyroscopic syst em involving mass, gyroscopic, iii stiffness, and rotational stiffness operators. This is the n conveniently discretized, along with the excitation forces and moments using Galerkin’s met hod as there are no matching boundary conditions as in the previous model. Basis func tio s used for the rotating model are global basis functions similar to that used in the n on-gyroscopic model. Natural frequency sensitivity to various system parameters such as t e rotational speed and mesh stiffness is determined and explained using modal strain en ergies. Response due to the loaded static transmission error is obtained by performing modal analysis after reducing the discretized system to a first order form. The study shows t hat the gyroscopic effect is present even for short lengths of the shafts. Natural freque ncy veering between flexural frequencies is present at low speeds and rare at high speeds wher e stiff ning due to rotational stress reduces the coupling between the shafts. For coupled frequencies, response of the system is found to be approximated by modal superposition of a smaller number of modes. The advantages of belt drives are low cost, easy maintenance , flexible locations of driver and driven shafts to name a few. Serpentine belt drives are wi d ly used in automobiles and heavy vehicles for driving accessories such as the alternat or, air conditioner, water pump, etc., by the engine power delivered from the crankshaft. The drive suffers from noise and belt tension fluctuation, which have their roots in the syste m vibration. At high rotation speeds, flexibility of the shafts attached to the pulleys pro vides additional degrees of freedom to the system. The mathematical model consists of the bel t modeled as a combination of extensional and torsional spring, which is justified for fl at, wide belts with high initial tension, having small bending stiffness. The compliant sha ft are attached to rigid pulleys which are connected by the belt in the reversed wrapped configuration . This hybrid discrete-continuous system consists of the shafts modeled as continuous elements while the pulleys with the attached belt modeled as discrete eleme nts. The mathematical model iv and the analysis are similar to the helical gear-shaft model , except that the helix angle is zero and the axis of the torsional spring is different. One of the pulleys is assumed to be attached to the crankshaft. Periodic load fluctuation from t he engine in the form of a force on the shaft attached to this pulley is considered and the res ponse in the form of tension fluctuation of the extensional spring is determined. The study provides practical guidance to the analysis and de sign engineers who consider the noise and vibration in gear and belt drives. Consid eration of shaft flexibility for specific design parameters makes the system free of secondar y sources of vibration induced noise and failure.

Computational methods of nonlinear tensioner damping in belt drive systems

Abstract: The friction type tensioner is an energy absorbing component in belt drive system which has hysteretic torque and nonlinear damping. In this paper, a hysteretic model is used for describing the tensioner’s operating torque versus the imposed angle, and considered into the dynamic analysis of a belt drive system. The modeling process for calculating the vibration responses of a belt drive system is presented, and two iterative methods are proposed for estimating the tensioner’s nonlinear damping in a varying excitation frequency. One timing belt drive system is taken as a case study. The system’s vibration responses, such as the oscillation angle of tensioner arm, the transmission error between pulleys and the hub load on pulley are calculated and compared with the measured values, which validate the presented methods. The influence of iterative method on the computational efficiency and iterative accuracy are both discussed. At last a modified method is presented to improve iterative efficiency. The presented technique can improve the computational efficiency with a good computational accuracy.