Modeling of the elastic mechanical behavior of thin compliant joints under load for highest-precision applications

For the most demanding measurement tasks in force metrology flexure hinges in compliant mechanisms represent a key component. To enhance the mechanical properties of devices like weighing cells, the ability of precise modeling of flexure hinges is essential. The present scientific work focuses on the modeling of the mechanical behavior of a single flexure hinge subjected to geometric deviations and non-ideal loading conditions as those encountered in weighing cells. The considered hinge has a semi-circular contour and a large width compared to its minimum notch height. This geometry is modeled using the finite element method. Requirements for a trustworthy and efficient computation are elaborated under the consideration of geometric deviations for later parametric studies. Analytical expressions found in the literature are compared to numerical results to prove the validity of their assumptions for thin hinges. The model is used for studying the deviation of the stiffness in non-ideal flexure hinges. Sources of deviation are identified and described by parameters. The range of values for each parameter is chosen on the basis of available manufacturing technology. Influential parameters are identified through a sensitivity analysis. The effect of loading conditions is studied in the context of the application in weighing cells. For the enhancement of the overall sensitivity, the stiffness of the flexure hinges can be reduced. One option, the alteration of the geometry by adding a flexure strip in the center of the semi-circular flexure hinge is studied in comparison to existing analytical equations. The effects of ground tilts for a single loaded flexure hinge are investigated as a foundation for future modeling of a tilt insensitive state of a weighing cell mechanism (autostatic state). By adjusting the vertical position of the center of mass of the lever, the tilt sensitivity can be reduced to zero. An approach to find the position for this state is presented considering the numerical limitations of finite element modeling. Using this approach, the variation of the sought position is evaluated for different values of the design parameters.Tesi

Diseño de un sistema de ventilación para estacionamiento subterráneo de tres niveles

El presente trabajo consiste en el diseño de un sistema de ventilación mecánica para un estacionamiento subterráneo de tres niveles, perteneciente a un edificio educativo universitario, con el fin de mantener la concentración de monóxido de carbono en el ambiente por debajo de 25 ppm, cumpliendo con los requerimientos de diversas normas internacionales. El sistema tiene como principio la ventilación general por depresión, con 30 rejillas de extracción distribuidas en cada piso. Para cada piso del estacionamiento se diseñó un sistema de extracción independiente. El caudal necesario para ventilar cada piso es de 9756 l/s para el primer sótano, 10365 l/s para el segundo sótano y 10975 l/s para el tercer sótano, siguiendo el método recomendado por la Asociación Americana de Ingenieros de Calefacción, Refrigeración y Aire Acondicionado (ASHRAE). Las dimensiones de los ductos se calcularon manteniendo la caída de presión por fricción constante en 0.650 Pa/m y manteniendo la velocidad del aire por debajo del límite recomendado por autores especializados. Se calcularon las caídas de presión, siendo la mayor caída de presión que se produce en el sistema de ductos de cada piso de 630.6 Pa en el primer sótano, 682.1 Pa en el segundo y 745.9 Pa en el tercero. Se seleccionaron los ventiladores que trabajen a las condiciones de caudal y presión dadas anteriormente, siendo todos ventiladores centrífugos con rotor de álabes inclinados hacia atrás trabajando a velocidades de 617 rpm para el sistema del primer sótano, 645 rpm para el segundo y 677 rpm para el tercero. A su vez, se seleccionaron los motores eléctricos que accionen los ventiladores. Los motores poseen potencias nominales de 11 kW para los sistemas del primer y segundo sótano, y 15 kW para el sistema del tercer sótano. Se seleccionó el sistema de transmisión por fajas trapezoidales para entregar la potencia a las velocidades del ventilador requeridas. Se diseñó el circuito de mando y potencia que arranque los motores mediante el método estrella-triángulo, cuando alguno de los sensores de monóxido de carbono detecte una concentración mayor a 25 ppm en cada uno de los niveles del estacionamiento. Además, se dimensionaron los conductores eléctricos, y los elementos de protección, adecuados para alimentar a los motores eléctricos según lo estipulado en el Código Nacional de Electricidad. Finalmente, se calculó el presupuesto del proyecto que asciende a US$ 155,386.97, incluyendo costos de ingeniería, equipos, materiales e instalación.Tesi

Synthesis of optimized compliant mechanisms for ultra-precision applications

Compliant mechanisms for ultra-precision applications are often required to achieve highest accuracy over largest possible ranges of motion along multiple axes. The typical synthesis approach for such high demands is based on the substitution of the revolute joints of a suitable rigid-body model with optimized flexure hinges. However, during the transition from rigid-body model to compliant mechanism, the effects of multiple input parameters are still widely unknown. Among them are the degrees of freedom of the rigid-body model, the integration of the drive elements, as well as the coupling of mechanisms to achieve multiple motion axes. The following contribution expands the fundamentals of the synthesis of compliant mechanisms based on rigid-body models for their application in ultra-precision technologies. Based on the investigation of the aforementioned parameters as well as the knowledge gained from previous research work, a novel synthesis method has been developed

Scaling of a compliant mechanism for high-precision force measurement applications

This paper is dedicated to the mechanical structure of a force transducer for the measurement of very small forces in the nanonewton range with highest resolution and lowest measurement uncertainty. To achieve this, a low stiffness in one direction of motion, but high stiffness in all other directions of motion is required. Existing solutions that meet the requirements are not suitable because of their overall dimensions. This results in a need for miniaturization. For this purpose, the scaling behavior of an existing monolithic compliant mechanism is investigated and it is verified which joint contour provides an optimal stiffness ratio. It is shown that the corner-filleted contour in general has lower bending stiffnesses, but also lower cross stiffnesses compared to the semi-circular contour. A nonlinear scaling effect for the ratio of bending stiffness and cross stiffness in corner-filleted contour offers optimization potential. Based on a simplified rigid body model, additionally, the miniaturization of the mechanism is optimized. The stiffness in the desired direction of motion is reduced by about 85% compared to a semi-circular contour. The result is promising for the further development of a miniaturized force transducer. The findings of this work contribute to the advancement of the measurement of low forces and offer new perspectives for future research in miniaturized force sensors

Investigation of a novel monolithic stiffness-compensated mechanism for high-precision load cells

Increasing demands in the fields of high-precision force measurement and weighing technology require an ever-higher measurement resolution, a larger measurement range, a lower measurement uncertainty, and traceability to a natural constant. Load cells using the compensation principle have the potential to fulfill these requirements. To enhance the measurement resolution and decrease the measurement uncertainty, the residual stiffness of the compliant mechanism in use needs to be compensated. Due to a lack of solutions in the state of the art, a novel monolithic stiffness-compensated mechanism for measurements according to the compensation principle was developed. Simulations show a stiffness reduction to 0.2%of the initial value, a theoretical force resolution of 31 pN, and applicability for any orientation in the gravity field. Experimental investigations on a prototype confirmed the existing potential. However, further optimization of the mechanism is required to negate the effects of manufacturing deviations

On Modeling the Bending Stiffness of Thin Semi-Circular Flexure Hinges for Precision Applications

Compliant mechanisms based on flexure hinges are widely used in precision engineering applications. Among those are devices such as precision balances and mass comparators with achievable resolutions and uncertainties in the nano-newton range. The exact knowledge of the mechanical properties of notch hinges and their modeling is essential for the design and the goal-oriented adjustment of these devices. It is shown in this article that many analytical equations available in the literature for calculating the bending stiffness of thin semi-circular flexure hinges cause deviations of up to 12% compared to simulation results based on the three-dimensional finite element model for the considered parameter range. A close examination of the stress state within the loaded hinge reveals possible reasons for this deviation. The article explains this phenomenon in detail and shows the limitations of existing analytical models depending on specific geometric ratios. An accurate determination of the bending stiffness of semi-circular flexure hinges in a wide range of geometric parameters without the need for an elaborate finite element analysis is proposed in form of FEM-based correction factors for analytical equations referring to Euler-Bernoulli’s beam theory

General and abdominal adiposity and hypertension in eight world regions: a pooled analysis of 837 population-based studies with 7·5 million participants

International audienceSummaryBackground Adiposity can be measured using BMI (which is based on weight and height) as well as indices of abdominal adiposity. We examined the association between BMI and waist-to-height ratio (WHtR) within and across populations of different world regions and quantified how well these two metrics discriminate between people with and without hypertension.MethodsWe used data from studies carried out from 1990 to 2023 on BMI, WHtR and hypertension in people aged 20–64 years in representative samples of the general population in eight world regions. We graphically compared the regional distributions of BMI and WHtR, and calculated Pearson’s correlation coefficients between BMI and WHtR within each region. We used mixed-effects linear regression to estimate the extent to which WHtR varies across regions at the same BMI. We graphically examined the prevalence of hypertension and the distribution of people who have hypertension both in relation to BMI and WHtR, and we assessed how closely BMI and WHtR discriminate between participants with and without hypertension using C-statistic and net reclassification improvement (NRI).FindingsThe correlation between BMI and WHtR ranged from 0·76 to 0·89 within different regions. After adjusting for age and BMI, mean WHtR was highest in south Asia for both sexes, followed by Latin America and the Caribbean and the region of central Asia, Middle East and north Africa. Mean WHtR was lowest in central and eastern Europe for both sexes, in the high-income western region for women, and in Oceania for men. Conversely, to achieve an equivalent WHtR, the BMI of the population of south Asia would need to be, on average, 2·79 kg/m² (95% CI 2·31–3·28) lower for women and 1·28 kg/m² (1·02–1·54) lower for men than in the high-income western region. In every region, hypertension prevalence increased with both BMI and WHtR. Models with either of these two adiposity metrics had virtually identical C-statistics and NRIs for every region and sex, with C-statistics ranging from 0·72 to 0·81 and NRIs ranging from 0·34 to 0·57 in different region and sex combinations. When both BMI and WHtR were used, performance improved only slightly compared with using either adiposity measure alone.InterpretationBMI can distinguish young and middle-aged adults with higher versus lower amounts of abdominal adiposity with moderate-to-high accuracy, and both BMI and WHtR distinguish people with or without hypertension. However, at the same BMI level, people in south Asia, Latin America and the Caribbean, and the region of central Asia, Middle East and north Africa, have higher WHtR than in the other regions

Diminishing benefits of urban living for children and adolescents’ growth and development

Optimal growth and development in childhood and adolescence is crucial for lifelong health and well-being1–6. Here we used data from 2,325 population-based studies, with measurements of height and weight from 71 million participants, to report the height and body-mass index (BMI) of children and adolescents aged 5–19 years on the basis of rural and urban place of residence in 200 countries and territories from 1990 to 2020. In 1990, children and adolescents residing in cities were taller than their rural counterparts in all but a few high-income countries. By 2020, the urban height advantage became smaller in most countries, and in many high-income western countries it reversed into a small urban-based disadvantage. The exception was for boys in most countries in sub-Saharan Africa and in some countries in Oceania, south Asia and the region of central Asia, Middle East and north Africa. In these countries, successive cohorts of boys from rural places either did not gain height or possibly became shorter, and hence fell further behind their urban peers. The difference between the age-standardized mean BMI of children in urban and rural areas was <1.1 kg m–2 in the vast majority of countries. Within this small range, BMI increased slightly more in cities than in rural areas, except in south Asia, sub-Saharan Africa and some countries in central and eastern Europe. Our results show that in much of the world, the growth and developmental advantages of living in cities have diminished in the twenty-first century, whereas in much of sub-Saharan Africa they have amplified

Worldwide trends in underweight and obesity from 1990 to 2022: a pooled analysis of 3663 population-representative studies with 222 million children, adolescents, and adults

Background: Underweight and obesity are associated with adverse health outcomes throughout the life course. We estimated the individual and combined prevalence of underweight or thinness and obesity, and their changes, from 1990 to 2022 for adults and school-aged children and adolescents in 200 countries and territories. Methods: We used data from 3663 population-based studies with 222 million participants that measured height and weight in representative samples of the general population. We used a Bayesian hierarchical model to estimate trends in the prevalence of different BMI categories, separately for adults (age ≥20 years) and school-aged children and adolescents (age 5-19 years), from 1990 to 2022 for 200 countries and territories. For adults, we report the individual and combined prevalence of underweight (BMI &lt;18·5 kg/m2) and obesity (BMI ≥30 kg/m2). For school-aged children and adolescents, we report thinness (BMI &lt;2 SD below the median of the WHO growth reference) and obesity (BMI &gt;2 SD above the median). Findings: From 1990 to 2022, the combined prevalence of underweight and obesity in adults decreased in 11 countries (6%) for women and 17 (9%) for men with a posterior probability of at least 0·80 that the observed changes were true decreases. The combined prevalence increased in 162 countries (81%) for women and 140 countries (70%) for men with a posterior probability of at least 0·80. In 2022, the combined prevalence of underweight and obesity was highest in island nations in the Caribbean and Polynesia and Micronesia, and countries in the Middle East and north Africa. Obesity prevalence was higher than underweight with posterior probability of at least 0·80 in 177 countries (89%) for women and 145 (73%) for men in 2022, whereas the converse was true in 16 countries (8%) for women, and 39 (20%) for men. From 1990 to 2022, the combined prevalence of thinness and obesity decreased among girls in five countries (3%) and among boys in 15 countries (8%) with a posterior probability of at least 0·80, and increased among girls in 140 countries (70%) and boys in 137 countries (69%) with a posterior probability of at least 0·80. The countries with highest combined prevalence of thinness and obesity in school-aged children and adolescents in 2022 were in Polynesia and Micronesia and the Caribbean for both sexes, and Chile and Qatar for boys. Combined prevalence was also high in some countries in south Asia, such as India and Pakistan, where thinness remained prevalent despite having declined. In 2022, obesity in school-aged children and adolescents was more prevalent than thinness with a posterior probability of at least 0·80 among girls in 133 countries (67%) and boys in 125 countries (63%), whereas the converse was true in 35 countries (18%) and 42 countries (21%), respectively. In almost all countries for both adults and school-aged children and adolescents, the increases in double burden were driven by increases in obesity, and decreases in double burden by declining underweight or thinness. Interpretation: The combined burden of underweight and obesity has increased in most countries, driven by an increase in obesity, while underweight and thinness remain prevalent in south Asia and parts of Africa. A healthy nutrition transition that enhances access to nutritious foods is needed to address the remaining burden of underweight while curbing and reversing the increase in obesity. Funding: UK Medical Research Council, UK Research and Innovation (Research England), UK Research and Innovation (Innovate UK), and European Union