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In this paper, a new method for the balancing of rotor-bearing systems supported on fluid film bearings is proposed. The influence coefficients necessary for balancing are calculated using a novel simulation method called the Numerical Assembly Technique. The advantages of this approach are quasi-analytical solutions for the equations of motion of complex rotor-bearing systems and very low computation times. The Numerical Assembly Technique is extended by speed-dependent stiffness and damping coefficients approximated by the short-bearing theory to model the behavior of rotor systems supported on fluid film bearings. The rotating circular shaft is modeled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, influence coefficients, eigenvalues, and the Campbell diagram of the rotor. These values are compared to simulations with the Finite Element Method to show the accuracy of the procedure. Two numerical examples of rotor-bearing systems are successfully balanced by the proposed balancing method.

The increasing demand for high-speed rotor-bearing systems results in the application of complex materials, which allow for a better control of the vibrational characteristics. This paper presents a model of a rotor including viscoelastic materials and valid up to high spin speeds. Regarding the destabilization of rotor-bearing systems, two main effects have to be investigated, which are strongly related to the associated internal and external damping of the rotor. For this reason, the internal material damping is modeled using fractional time derivatives, which can represent a large class of viscoelastic materials over a wide frequency range. In this paper, the Numerical Assembly Technique (NAT) is extended for the rotating viscoelastic Timoshenko beam with fractional derivative damping. An efficient and accurate simulation of the proposed rotor-bearing model is achieved. Several numerical examples are presented and the influence of internal damping on the rotor-bearing system is investigated and compared to classical damping models.

Vibration in rotating machinery leads to a series of undesired effects, e.g. noise, reduced service life or even machine failure. Even though there are many sources of vibrations in a rotating machine, the most common one is mass unbalance. Therefore, a detailed knowledge of the system behavior due to mass unbalance is crucial in the design phase of a rotor-bearing system. The modelling of the rotor and mass unbalance as a lumped system is a widely used approach to calculate the whirling motion of a rotor-bearing system. A more accurate representation of the real system can be found by a continuous model, especially if the mass unbalance is not constant and arbitrarily oriented in space. Therefore, a quasi-analytical method called Numerical Assembly Technique is extended in this paper, which allows for an efficient and accurate simulation of the unbalance response of a rotor-bearing system. The rotor shaft is modelled by the Rayleigh beam theory including rotatory inertia and gyroscopic effects. Rigid discs can be mounted onto the rotor and the bearings are modeled by linear translational/rotational springs/dampers, including cross-coupling effects. The effect of a constant axial force or torque on the system response is also examined in the simulation.

Due to growing demands on newly developed products concerning their weight, sound emission, etc., advanced materials are introduced in the product designs. The modeling of these materials is an important task, and a very promising approach to capture the viscoelastic behavior of a broad class of materials are fractional time derivative operators, since only a small number of parameters is required to fit measurement data. The fractional differential operator in the constitutive equations introduces additional challenges in the solution process of structural models, e.g., beams or plates. Therefore, a highly efficient computational method called Numerical Assembly Technique is proposed in this paper to tackle general beam vibration problems governed by the Timoshenko beam theory and the fractional Zener material model. A general framework is presented, which allows for the modeling of multi-span beams with general linear supports, rigid attachments, and arbitrarily distributed force and moment loading. The efficiency and accuracy of the method is shown in comparison to the Finite Element Method. Additionally, a validation with experimental results for beam systems made of steel and polyvinyl chloride is presented, to illustrate the advantages of the proposed method and the material model.

The increasing use of high-speed machinery leads to a growing demand for efficient balancing methods for flexible rotors. Conventional balancing methods are costly and time-consuming since they require multiple trial runs. For this reason, recent research focuses on model-based balancing methods, which substitute measurements with simulations. This work presents and examines a model-based modal balancing method, which utilizes the Numerical Assembly Technique (NAT) for the in situ balancing of warped rotors with flexible behaviour. NAT is a successive modification of discrete–continuous modelling that leads to analytical harmonic solutions and is very computationally efficient. In this version of NAT, internal damping is also included with a viscoelastic material model using fractional time derivatives. The modal balancing procedure is adapted to handle measurements outside of the critical speeds and the effect of the pre-bend on the rotor. The accuracy of the simulations is shown by comparing measured mode shapes and eigenvalues with values calculated with NAT. Furthermore, the first two modes of a rotor test bed are successfully balanced without trial runs.

In order to analyze the dynamics of a structural problem accurately, a precise model of the structure, including an appropriate material description, is required. An important step within the modeling process is the correct determination of the model input parameters, e.g., loading conditions or material parameters. An accurate description of the damping characteristics is a complicated task, since many different effects have to be considered. An efficient approach to model the material damping is the introduction of fractional derivatives in the constitutive relations of the material, since only a small number of parameters is required to represent the real damping behavior. In this paper, a novel method to determine the damping parameters of viscoelastic materials described by the so-called fractional Zener material model is proposed. The damping parameters are estimated by matching the Frequency Response Functions (FRF) of a virtual model, describing a beam-like structure, with experimental vibration data. Since this process is generally time-consuming, a surrogate modeling technique, named Polynomial Chaos Expansion (PCE), is combined with a semi-analytical computational technique, called the Numerical Assembly Technique (NAT), to reduce the computational cost. The presented approach is applied to an artificial material with well defined parameters to show the accuracy and efficiency of the method. Additionally, vibration measurements are used to estimate the damping parameters of an aluminium rotor with low material damping, which can also be described by the fractional damping model.

In this paper, a new application of the Numerical Assembly Technique is presented for the balancing of linear elastic rotor-bearing systems with a stepped shaft and arbitrarily distributed mass unbalance. The method improves existing balancing techniques by combining the advantages of modal balancing with the fast calculation of an efficient numerical method. The rotating stepped circular shaft is modelled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, eigenvalues and the associated mode shapes of the rotor. The displacements of a simulation are compared to measured displacements of the rotor-bearing system to calculate the generalized unbalance for each eigenvalue. The generalized unbalances are modified according to modal theory to calculate orthogonal correction masses. In this manner, a rotor-bearing system is balanced using a single measurement of the displacement at one position on the rotor for every critical speed. Three numerical examples are used to show the accuracy and the balancing success of the proposed method.

The production of Electric Vehicles (EVs) has a significant environmental impact, with up to 50 % of their lifetime greenhouse gas potential attributed to manufacturing processes. The use of sustainable materials in EV design is therefore crucial for reducing their overall carbon footprint. Wood laminates have emerged as a promising alternative due to their renewable nature. Additionally, wood-based materials offer unique damping properties that can contribute to improved Noise, Vibration, and Harshness (NVH) characteristics. Compared to conventional materials such as aluminium, wooden structures exhibit significantly higher damping properties. In this study, the potential of lightweight wood composites, specifically steel-wood hybrid structures, is investigated as a potential composite material for battery housings for electric vehicles. Experiments have been performed in order to determine the modal parameters, such as natural frequencies and damping ratios. These parameters where used to validate a free-free steel-wood hybrid beam simulation model. The numerical model was subsequently used to analyse the effect of the wood–steel adhesive on the natural frequencies and to compare a steel-wood hybrid battery housing to a aluminium based battery housing. The presented results in conjunction with literature data demonstrate that steel-wood hybrid structures can provide attractive stiffness properties at low weights while utilizing the excellent damping properties inherent in plywood. These properties can contribute to an improved noise and vibration behaviour, which could improve passenger comfort while reducing the life cycle greenhouse gas potential of the structural battery pack components by up to 50 %. The utilization of steel-wood hybrid structures within the battery pack of an EV may also contribute to a reduction in vibration-induced cell degradation, attributed to the higher damping characteristics inherent in these composite materials. This research contributes to the field of sustainable EV design by exploring the advantages of wood composites in the context of NVH optimization. The utilization of steel-wood hybrid structures represents a novel approach to exploit the unique properties of both materials, combining stiffness and damping characteristics. This study offers a pathway towards reducing the environmental impact of EV production while improving the NVH performance of electric vehicles, by incorporating sustainable materials like wood laminates into battery pack design.