A general framework for crankshaft balancing and counterweight design

In the automotive field, the requirements in terms of carbon emissions and improved efficiency are shifting the focus of designers towards reduced engine size. As a result, the dynamic balancing of an engine with strict limitations on the number of cylinders, the weight and the available space becomes a challenging task. The present contribution aims at providing the designer with a tool capable of selecting fundamental parameters needed to correctly balance an internal combustion engine, including the masses and geometry of the elements to be added directly onto the crankshaft and onto the balancing shafts. The relevant elements that distinguish the tool from others already proposed are two. The first is the comprehensive matrix formulation which makes the tool fit for a wide variety of engine configurations. The second is an optimisation procedure that selects not only the position of the mass and centre of gravity of the counterweight but also its complete geometric configuration, thus instantaneously identifying the overall dimensions and weight of the crankshaft

Forced response prediction of turbine blades with flexible dampers: the impact of engineering modelling choices

This paper focuses on flexible friction dampers (or “strips”) mounted on the underside of adjacent turbine blade platforms for sealing and damping purposes. A key parameter to ensure a robust and trustworthy design is the correct prediction of the maximum frequency shift induced by the strip damper coupling adjacent blades. While this topic has been extensively addressed on rigid friction dampers, both experimentally and numerically, no such investigation is available as far as flexible dampers are concerned. This paper builds on the authors’ prior experience with rigid dampers to investigate the peculiarities and challenges of a robust dynamic model of blade-strips systems. The starting point is a numerical tool implementing state-of-the-art techniques for the efficient solution of the nonlinear equations, e.g., multi-harmonic balance method with coupled static solution and state-of-the-art contact elements. The full step-by-step modelling process is here retraced and upgraded to take into account the damper flexibility: for each step, key modelling choices (e.g., mesh size, master nodes selection, contact parameters) which may affect the predicted response are addressed. The outcome is a series of guidelines which will help the designer assign numerical predictions the proper level of trust and outline a much-needed experimental campaign

Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

Background The presence of parametric excitation in dynamic structures, caused by friction, crack, varying compliance, electromagnetic field, etc. may generate unbounded responses. In the literature there exist several numerical analyses of systems affected by parametric excitation, while experimental studies are less frequent. Objective The goal of the paper is to create a demonstrator of a parametrically excited system, whose stability can be modified through a controlled physical parameter. This work also investigates the applicability of the recently developed stability analysis method named Jacobian Based Approach (JBA). Methods This paper studies a simple experimental set-up comprising of a cantilever beam mounted on a spring with time - varying stiffness, achieved through the use of an electromagnet. The test rig allows measuring directly the magnetic force without any preknowledge of the values of electrical parameters. Results obtained from the test rig are compared with numerical results obtained from the Finite Element model. In this study, Hill's method and JBA are employed to obtain the stability plot highlighting the regions of parametric instabilities. Results Good agreement is found between experimental and numerical data and the presence of unstable behavior is verified through the use of the well - known Hill's method and the JBA. Furthermore, this study demonstrates that the stability plot, highlighting the unstable regions, computed by JBA is in complete agreement with the one obtained by Hill's method. Conclusions It is shown how the parametric instability can be triggered through the regulation of a simple physical parameter, i.e. the gap between the electromagnet and the beam. The numerical model analyzed by the ad - hoc technique proposed by the authors i.e. JBA has been proven to have predictive capabilities in studying a system under parametric excitation and could be a potential substitution for state-of-the-art stability analysis techniques such Hill's method

Latest Investigations on Underplatform Damper inner Mechanics

Underplatform dampers (UPDs) are widely used as a source of friction damping and are frequently incorporated into compressors and turbines for both aircraft and power-plant applications to mitigate the effects of resonant vibrations on fatigue failure. Due to the nonlinear nature of dry friction, in general dynamic analysis of structures constrained through frictional contacts is difficult, direct time integration with commercial finite element codes may not be a suitable choice given the large computation times. For this reason, ad hoc numerical codes have been developed in the frequency domain. Some authors prefer a separate routine in order to compute contact forces as a function of input displacements, others include the damper in the FE model of the bladed array. All numerical models, however, require knowledge or information of contact -friction parameters, which are established either through direct frictional measurements, done with the help of single contact test arrangements, or by fine tuning the parameters in the numerical model and comparing the experimental response of damped blade against its computed response. The standard approach is to fine-tune and experimentally validate the UPDs models by comparing measured and calculated vibration response of blade pairs. To our knowledge, nobody has ever attempted to directly measure the forces transmitted between the platforms through the damper and the relative damper-platform movement. In the light of recent results from direct measurements on dampers it is evident that a dedicated routine for the damper mechanics is an effective tool to capture those finer details which are essential to an appropriate description of damper behaviour. This was made possible by the successful effort of the present authors to accurately measure the forces transmitted between the platforms through the damper, to connect them with the relative platforms movement and to use the findings for the validation of the numerical model. The cross-comparison between numerical and experimental results allows to gain a clear understanding of all contact events (stick, slip, lift) which take place during the cycle, and on how they influence the damping performance

Numerical and experimental investigations on underplatform damper mechanics

So called under-platform dampers are widely used as a source of friction damping to mitigate resonance in gas turbine blades and avoid service failures. Due to the high computational cost of performing dynamic analysis of structures constrained through frictional contacts, ad hoc numerical codes have been developed in the frequency domain. Whatever the numerical model, it requires knowledge of contact-friction parameters, which are established either through single contact frictional measurements, or by tuning the damper parameters though comparison of the experimental response of damped blade against its computed response or, else, by fine tuning the damper parameters by comparing the measured v. the calculated hysteresis cycle. The last one is these authors’ choice. Equipment and method are described accordingly

Bariatric surgery in an obese patient with Albright hereditary osteodystrophy: a case report

INTRODUCTION: We report for the first time the case of a patient with Albright hereditary osteodystrophy and pseudopseudohypoparathyroidism who underwent a Roux-en-Y gastric bypass. CASE PRESENTATION: A 26-year-old obese Caucasian woman with Albright hereditary osteodystrophy with pseudopseudohypoparathyroidism (heterozygous mutation (L272F) in GNAS1 exon 10 on molecular analysis) was treated with gastric bypass. She had the classical features of Albright hereditary osteodystrophy: short stature (138cm), obesity (body mass index 49.5kg/m2), bilateral shortening of the fourth and fifth metacarpals, short neck, round and wide face with bombed front and small eyes. Before the gastric bypass was performed, biochemical determination revealed a slightly low serum calcium level (2.09mmol/L; normal range 2.1 to 2.5mmol/l), and an elevated parathyroid hormone level (87ng/L; normal range 10 to 70ng/L) associated with low vitamin D level (19μg/L; normal range 30 to 50μg/L). Vitamin D supplementation was prescribed before surgery. After the Roux-en-Y gastric bypass, she achieved a progressive substantial weight loss, from 94kg (body mass index 49.5kg/m2) to 49kg (body mass index 25.9kg/m2) in one year. Her weight then stabilized at 50kg (body mass index 26kg/m2) during our three years of follow-up. Before the operation and every three months after it, she was screened for nutritional deficiencies, and serum markers of bone turnover and renal function were monitored. Considering the deficiencies in zinc, magnesium, calcium, vitamin D and vitamin B12, appropriate supplementation was prescribed. Before and two years after the Roux-en-Y gastric bypass, a dual-energy X-ray absorptiometry assessment of bone density was performed that showed no changes on her lumbar column (0.882g/cm2 and both T-score and Z-score of -1.5 standard deviation). In addition, bone microarchitecture with a measurement of her trabecular bone score was found to be normal. CONCLUSION: This is the first case of Roux-en-Y gastric bypass described in a patient with pseudopseudohypoparathyroidism showing that such a procedure seems to be safe in obese patients with Albright hereditary osteodystrophy and pseudopseudohypoparathyroidism if appropriately followed up. As obesity is a prominent feature of Albright hereditary osteodystrophy, such patients might seek bariatric surgery. After a Roux-en-Y gastric bypass, patients with Albright hereditary osteodystrophy associated with pseudopseudohypoparathyroidism need long-term follow-up on nutritional and metabolic issues