An alternative formulation of the dynamic transmission error to study the oscillations of automotive hypoid gears

A new modelling approach on the torsional dynamics of hypoid gear pairs is presented in this work. The current formulation is characterised by an alternative expression of the Dynamic Transmission Error (DTE), accounting for the variation of the effective mesh position. Speed dependent resistive torque is introduced on the gear wheel, enabling the system to reach dynamic equilibrium based on realistic vehicle operating conditions. The above are supplementing past research studies, where simplifications were introduced in the calculation of DTE, while the operating angular velocity was defined a priori. The analysis is accompanied by numerical results, indicating the rich dynamic behavior captured by the new formulation. The dynamic complexity of the system necessitates the identification of the various response regimes. A solution continuation method (software AUTO) is employed to follow the stable/unstable periodic response branches over the operating range of the differential under examination

Hybrid Photothermal Technique for Microscale Thermal Conductivity Measurement

Most existing thermal conductivity measurement techniques of nuclear fuel only measure the overall effective thermal conductivity of the fuel, cladding, and gap, with low spatial-resolution. However, damage to nuclear fuel microstructure caused by neutron-irradiation can result in sharp, local changes of thermal conductivity. Additionally, extremely large temperature-gradients (~1600 K/cm) from the fuel centerline to the coolant result in similar gradients of thermal conductivity. Therefore, in pursuit of greater understanding of nuclear fuel performance, the objective of this study was to develop a non-contact thermal conductivity measurement technique to provide micron-sized spatial-resolution capability. Based on photothermal techniques and using both frequency and spatial-domain photothermal reflectance methods, an experimental measurement system was designed, built, and tested for measuring the thermal conductivity of a thin-film coated material with micron resolution. This hybrid method involves separate measurement of thermal diffusivity, D, and thermal effusivity, e, from which, thermal conductivity, k = (e2/D)1/2 is calculated. A detailed parametric analysis using analytical solutions and a numerical model has been performed to guide the experiment and optimize measurement conditions. The measurement system was validated using two calibration samples having thermal conductivities at both the upper and lower limit of the common range of nuclear fuels (~1 - 10 W/m/K). Sources of experimental errors are discussed qualitatively and the uncertainty of the measurement system for the thermal conductivity range of interest is quantified. The measured error is found to be about 10%, and up to close to 20% for the worst case (upper limit of k range). An extended application of the modulated laser excitation technique is explored to measure mechanical properties of solid materials. This technique involves obtaining the natural frequencies of different vibrational modes of a cantilever beam sample allowing for the extraction of the elasticity constants of the material. From Neumann\u27s principle, the number of independent elasticity constants is dependent on the symmetry of the material structure. Specifically, symmetries of crystalline materials and composite materials are analyzed. Experimental results of two validation samples with cubic crystal system agreed well with the published values with experimental errors of ~10%

The elastic wave propagation in rectangular waveguide structure determination of dispersion curves and their application in nondestructive techniques

The use of mechanic waves for assessing structural integrity is a well-known non-destructive technique (NDT). The ultrasound applied in the guided wave in particular requires significant effort in order to understand the complexities of the propagation so as to develop new methods in damage detection, in this case, knowing the interaction between the wave propagation and the geometry of the waveguides is mandatory. In the present work, the wave propagation in rectangular steel rod is presented. In this study, the section dimensions were fixed as 5 × 15 [mm], a typical element of the flexible riser structural amour commonly used in the offshore oil industry. The studies here presented were restricted to [0, 100 KHz] frequencies. This frequency interval is in the range of commercial waveguide equipment commonly applied in ducts in NDT applications. The computation of the dispersion curves is performed by using three different methodologies: (i) analytical solutions, (ii) a method that combines analytical approaches with finite element methods (SAFE), and (iii) experimental method that extracted information from the rod using laser vibrometers and piezoelectric actuators. Finally, two applications based on the dispersion curves determined in the rectangular waveguide are presented to illustrate the possibilities of the curve dispersion knowledge related to the specific geometry in the development and application linked to NDT. The first application consists on showing the possibilities of the techniques that use a fiber grating Bragg cell (FGB) to measure the wave displacement and the second application involves the simulation of pre-fissured prismatic waveguide aimed at searching to induce three characteristic acoustic events. The model was built combining the finite element method and a version of the discrete element method

Tribo-dynamic analysis of hypoid gears in automotive differentials

Torsional vibrations in differentials of Rear Wheel Drive vehicles are of major importance for the automotive industry. Hypoid transmissions, forming the motion transfer mechanism from the driveshaft to the wheels, suffer from severe vibration issues. The latter are attributed to improper mesh between the mating gear flanks due to misalignments, variation of contact load and shifting of the effective mesh position. For certain operating conditions, the gear pair exhibits high amplitude motions accompanied with separation of the mating surfaces. Ultimately, single or even double-sided vibro-impact phenomena evolve, which have been related to noise generation. This thesis attempts to address these issues by effectively analysing the dynamic behaviour of a hypoid gear pair under torsional motion. The case study considered is focused on a commercial light truck. The major difference of the employed mathematical model to prior formulations is the usage of an alternative expression for the dynamic transmission error so that the variation of contact radii and transmission error can be accounted for. This approach combined to a correlation of the resistive torque in terms of the angular velocity of the differential enables the achievement of steady state, stable periodic solutions. The dynamic complexity of systems with gears necessitates the identification of the various response regimes. A solution continuation method (software AUTO) is employed to determine the stable/unstable branches over the operating range of the differential. The ensuing parametric studies convey the importance of the main system parameters on the dynamic behaviour of the transmission yielding crucial design guidelines. A tribo-dynamic investigation aims at expanding the dynamic model from pure dry conditions to a more integrated elastohydrodynamic (EHL) approach. Analytical and extrapolated solutions are applied for the derivation of the film thickness magnitude based on the kinematic and loading characteristics of the dynamic model. The temperature rise is governed mainly by conduction due to the thin lubricant films. The generated friction is also computed as a function of the viscous shear and asperity interactions. The effective lubricant viscosity is greatly affected by the pressure increase due to the resonant behaviour of the contact load. The final part of this work is involved with a feasibility study concerning the application of Nonlinear Energy Sinks (NES) as vibration absorbers, exploiting their ability for broadband frequency interaction. Response regimes associated with effective energy absorption are identified and encouraging results are obtained, showing the potential of the method

The elasticwave propagation in rectangular waveguide structure: Determination of dispersion curves and their application in nondestructive techniques

The use of mechanic waves for assessing structural integrity is a well-known non-destructive technique (NDT). The ultrasound applied in the guided wave in particular requires significant effort in order to understand the complexities of the propagation so as to develop new methods in damage detection, in this case, knowing the interaction between the wave propagation and the geometry of the waveguides is mandatory. In the present work, the wave propagation in rectangular steel rod is presented. In this study, the section dimensions were fixed as 5 x 15 [mm], a typical element of the flexible riser structural amour commonly used in the offshore oil industry. The studies here presented were restricted to [0, 100 KHz] frequencies. This frequency interval is in the range of commercial waveguide equipment commonly applied in ducts in NDT applications. The computation of the dispersion curves is performed by using three different methodologies: (i) analytical solutions, (ii) a method that combines analytical approaches with finite element methods (SAFE), and (iii) experimental method that extracted information from the rod using laser vibrometers and piezoelectric actuators. Finally, two applications based on the dispersion curves determined in the rectangular waveguide are presented to illustrate the possibilities of the curve dispersion knowledge related to the specific geometry in the development and application linked toNDT. The first application consists on showing the possibilities of the techniques that use a fiber grating Bragg cell (FGB) to measure the wave displacement and the second application involves the simulation of pre-fissured prismatic waveguide aimed at searching to induce three characteristic acoustic events. The model was built combining the finite element method and a version of the discrete element method

A comparative and parametric study of experimentally obtained flutter derivatives of four bridge decks - streamlined and bluff shapes

Predicting instability for flexible structures has always been a crucial activity in the science of aeroelasticity. Instability for actual structures, such as bridge decks, can be predicted by extracting flutter derivatives from a wind tunnel section model study. A variety of methods have been employed to extract flutter derivatives including free-vibration, forced-oscillation, and computational fluid dynamics. A recent technique developed in the Iowa State University Wind Simulation and Testing Laboratory (ISU WiST Lab) utilizes a three degree-of-freedom (DOF) free-vibration suspension system for data acquisition and the Iterative Least Squares method incorporated with System Identification (ILS System ID) software for data analysis. Validation of this technique was critical for establishing confidence in the obtained flutter derivatives. Another important aspect of wind tunnel testing is the ability to develop realistic models capable of providing means to obtain reliable pressure and/or force data while maintaining rigidity and minimal weight. The purpose of this research was to scrutinize the free-vibration technique used in the ISU WiST Lab to offer improvements to the system and techniques used for data acquisition and analysis and to contribute new model building methods for future testing. The system verification involved design and construction of bridge deck section models, acquiring displacement time histories from wind tunnel testing, analyzing the acquired data with an improved version of the ILS System ID software, and finally comparing obtained flutter derivatives through an assortment of means. The parametric study involved comparing flutter derivative data between stable and unstable bridge decks, longer and shorter section model lengths, and solid-streamlined versus slotted-streamlined bridge decks. These studies helped to illustrate the importance of bridge design for stability and model design for proper analysis. For the comparative study, bridge models were tested in two separate single DOF cases (vertical and then torsional) and a two DOF case (vertical and torsional). In all eight flutter derivatives were extracted, four being direct flutter derivatives. The direct flutter derivatives were compared between the single DOF cases and the two DOF case as well as with data from outside sources to establish further confidence in system operation

Dynamic and static analyses of continuous curved composite multiple-box girder bridges.

Horizontally curved concrete deck on multiple steel box girder bridges is a structurally efficient, economic, and aesthetically pleasing method of supporting curved roadway systems. Modern highway constructions are often in need of bridges with horizontally curved alignments due to the tight geometry restrictions. Continuous curved composite box girder bridges allow for the use of longer spans, thus reducing costs of the substructure. Despite all inherent advantages of continuous curved composite box girder bridges, they do pose challenging problems for engineers in calculating the load distribution due to moving vehicles across the bridges. Curved bridges are subjected to high torsional as well as flexural stresses. The interaction between the box girders is also more complicated in curved bridges than that in straight bridges. North American codes for bridges have recommended expressions for the load distribution factors only for straight bridges and not for curved bridges. Impact factors proposed in these codes are generally restricted also to straight bridges. In addition, simplified formula to predict the fundamental frequency of analyzing the bridges is not available. To assist engineers in dealing with the complexities of continuous curved composite box girder bridges, a reliable, accurate, and simple method is required to calculate the structure\u27s response under self-weight and vehicular loading. The refined three-dimensional finite-element analysis method is employed to investigate the static and dynamic responses of the bridge. Two two-equal-span two-box physical bridge models were constructed in the laboratory. One of the bridge models was straight in plan while the other was horizontally curved. The physical models were tested under several static loading cases to better comprehend their elastic behaviour. Free-vibration tests were also conducted to obtain the natural frequencies and the corresponding mode shapes of the bridge models. Both models were loaded up to failure to examine the collapse mechanism and its correlation with the finite element modeling. Findings obtained from the two physical bridge models were compared to those predicted by the analytical models. The agreement between the finite element model and the experimental model made it possible to use the analytical models to conduct three parametric studies on several bridges.Dept. of Civil and Environmental Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .S26. Source: Dissertation Abstracts International, Volume: 65-07, Section: B, page: 3593. Advisers: J. Kennedy; K. Sennah. Thesis (Ph.D.)--University of Windsor (Canada), 2004

Vibration energy harvester for variable speed rotor applications using passively self-tuned beams

A vibration energy harvester is proposed for rotating systems based on transverse vibrations of an assembly of thin beams and electromagnetic interaction of a carried magnet with a coil of wire. The harvester is designed in a way such that centrifugal forces are utilized to tune the system’s natural frequency to the expected frequency of torsional vibrations. In fact, a novel combination of a tuning mass positioned at the beam’s support and an applied preload are introduced to establish a tuning mechanism that is capable of maintaining resonance along a wide frequency range. The device’s tuning can cover relatively high rotor speeds, overcoming previous limitations on the size and the physics of tuning via axial loads. Moreover, exact expressions of the beams’ mode shapes are taken into account to improve the accuracy of the proposed tuning mechanism. Numerical simulations of the device’s response are carried out for case studies corresponding to different frequency orders. It is shown that the system can maintain a flat power output across a wide range of operating speeds, effectively leading to purely broadband energy harvesting

Updating Finite Element Model of a Wind Turbine Blade Section Using Experimental Modal Analysis Results

This paper presents selected results and aspects of the multidisciplinary and interdisciplinary research oriented for the experimental and numerical study of the structural dynamics of a bend-twist coupled full scale section of a wind turbine blade structure. The main goal of the conducted research is to validate finite element model of the modified wind turbine blade section mounted in the flexible support structure accordingly to the experimental results. Bend-twist coupling was implemented by adding angled unidirectional layers on the suction and pressure side of the blade. Dynamic test and simulations were performed on a section of a full scale wind turbine blade provided by Vestas Wind Systems A/S. The numerical results are compared to the experimental measurements and the discrepancies are assessed by natural frequency difference and modal assurance criterion. Based on sensitivity analysis, set of model parameters was selected for the model updating process. Design of experiment and response surface method was implemented to find values of model parameters yielding results closest to the experimental. The updated finite element model is producing results more consistent with the measurement outcomes

The study of the self-damping properties of overhead transmission line conductors subjected to wind-induced oscillations.

Doctoral Degree. University of KwaZulu-Natal, Durban.Conductors are flexible, elastic structural components of power lines. The relatively high flexibility of the conductors, coupled with the long spans and the axial tension, makes conductors to be highly prone to dynamic excitation such as wind loading. The problem of the dynamic behavior of overhead power transmission line conductors under the action of wind and other forms of excitations is very important, since it proffers the optimal design of the line in terms of its dynamic characteristics. Thus, mechanical vibration of power lines needs to be mitigated, especially from aeolian vibration as they can lead to damage of the lines causing power interruptions. The dynamic behaviour of conductors can be influenced by its damping. However, available tools for the analysis of this phenomenon is scarce. The objective of this study is to evaluate the conductor self-damping. The goal is to characterize and ascertain the influence of various conductors’ parameters on the amount of energy dissipation. In this study, a numerically based investigation of the response of conductors was carried out i.e. finite element analysis (FEA or FEM). This was used to model the conductor using a new modeling approach, in which the layers of its discrete structure of helical strands were modelled as a composite structure. Due to the helical structure of the conductor strands, this give rise to inter-strands contacts. During bending caused by external loading, the stick-slip phenomenon does occur around the contact region resulting in damping of energy out of the system. Characterizing the damping mechanism as hysteresis phenomenon, this resulted from coulomb’s dry-friction with the stick-slip regime at contacts points between the conductor strands. Employing contact mechanics to characterize and the use of FEM to discretize these contact regions, parameters such as the contact forces, strain and stress were established. When the conductor experiences a dynamic excitation in a sinusoidal form, a hysteresis loop is formed. The use of contact region parameters, to evaluate the area of the hysteresis loop and the area of the loop determines the amount of self-damping. Experimental studies were conducted to validate the FEM model. Two forms of experiment were done. The first was the sweep test, done at a specified axial tension i.e. as a function of its ultimate tensile strength. This was used to determine the resonance frequencies for the conductors. In the second test, using the determined resonance frequencies from the first test were used to vibrate the conductors at these frequencies to establish the hysteresis loop at the same specified axial tension. The experiment was conducted with four different conductors with different number of layers. This was used to establish the relation between the numbers of layer and the amount of damping from the conductor. The conductors’ vibration experimental results obtained at a defined axial tension (as percentage of its UTS) correlate with that of FEM model. The results obtained showed a general increase in the resonance frequencies of vibration and a decrease in damping as the axial tension of the conductor is increased. The establishment of the hysteretic constitutive behaviour of strands under specific loading conditions as described in the thesis, using this FEM model, an algorithm was developed to evaluate the conductor self-damping. Based on this algorithm, computer programs have been developed to evaluate the conductor’s dynamic behaviour and implemented in MATLAB environment. Due to the very close relation between damping and conductor fatigue, this model can also be extended to investigate fatigue failure of conductors