Applied Mathematics to Mechanisms and Machines

This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics

Advances in Mechanical Systems Dynamics 2020

The fundamentals of mechanical system dynamics were established before the beginning of the industrial era. The 18th century was a very important time for science and was characterized by the development of classical mechanics. This development progressed in the 19th century, and new, important applications related to industrialization were found and studied. The development of computers in the 20th century revolutionized mechanical system dynamics owing to the development of numerical simulation. We are now in the presence of the fourth industrial revolution. Mechanical systems are increasingly integrated with electrical, fluidic, and electronic systems, and the industrial environment has become characterized by the cyber-physical systems of industry 4.0. Within this framework, the status-of-the-art has become represented by integrated mechanical systems and supported by accurate dynamic models able to predict their dynamic behavior. Therefore, mechanical systems dynamics will play a central role in forthcoming years. This Special Issue aims to disseminate the latest research findings and ideas in the field of mechanical systems dynamics, with particular emphasis on novel trends and applications

Radar Imaging with a Network of Digital Noise Radar Systems

Today\u27s battlefield consists of a blend of humans and machines working together to locate and monitor the enemy. Due to the threat of terrorism, today\u27s enemy can be anyone and they can exist anywhere even in populated cities. Monitoring human activities in an urban environment is a difficult problem due to walls, clutter, and other obstructions. This thesis focused on developing a network of digital noise radar sensors that could operate simultaneously to track humans and non-human targets inside rooms and through walls. The theory, application, and results are discussed throughout this thesis. A noise radar works by cross correlating the received signal with a time delayed replica of the transmit signal. A high correlation indicates a target. A digital noise radar digitizes the transmit and receive signals and accomplishes the correlation in software. A network of three digital noise radars was constructed to triangulate the (x, y) position of a target within a room. The results were presented in two-dimensional graphs. In nine out of ten cases the stationary targets were clearly identified. In eight out of ten cases the stationary targets were located within the range solution of the system, 0.375 m. In the one miss case, the results image indicated the presence of the human target, but the detection was faint and possible to miss. Tests were also accomplished with moving human targets. In these tests the network of radar systems tracked the human target in an empty and cluttered room until the target was out of range. The test results prove that a network of simultaneously operating noise radars can locate and track human and non-human targets within rooms

Modeling and Implementation of Wireless Sensor Networks for Logistics Applications

Logistics has experienced a long time of developments and improvements based on the advanced vehicle technologies, transportation systems, traffic network extension and logistics processes. In the last decades, the complexity has increased significantly and this has created complex logistics networks over multiple continents. Because of the close cooperation, these logistics networks are highly dependent on each other in sharing and processing the logistics information. Every customer has many suppliers and vice versa. The conventional centralized control continues but reaches some limitations such as the different distribution of suppliers, the complexity and flexibility of processing orders or the dynamics of the logistic objects. In order to overcome these disadvantages, the paradigm of autonomous logistics is proposed and promises a better technical solution for current logistics systems. In autonomous logistics, the decision making is shifted toward the logistic objects which are defined as material items (e.g., vehicles, containers) or immaterial items (e.g., customer orders) of a networked logistics system. These objects have the ability to interact with each other and make decisions according to their own objectives. In the technical aspect, with the rapid development of innovative sensor technology, namely Wireless Sensor Networks (WSNs), each element in the network can self-organize and interact with other elements for information transmission. The attachment of an electronic sensor element into a logistic object will create an autonomous environment in both the communication and the logistic domain. With this idea, the requirements of logistics can be fulfilled; for example, the monitoring data can be precise, comprehensive and timely. In addition, the goods flow management can be transferred to the information logistic object management, which is easier by the help of information technologies. However, in order to transmit information between these logistic objects, one requirement is that a routing protocol is necessary. The Opportunistic relative Distance-Enabled Uni-cast Routing (ODEUR ) protocol which is proposed and investigated in this thesis shows that it can be used in autonomous environments like autonomous logistics. Moreover, the support of mobility, multiple sinks and auto-connection in this protocol enhances the dynamics of logistic objects. With a general model which covers a range from low-level issues to high-level protocols, many services such as real time monitoring of environmental conditions, context-aware applications and localization make the logistic objects (embedded with sensor equipment) more advanced in information communication and data processing. The distributed management service in each sensor node allows the flexible configuration of logistic items at any time during the transportation. All of these integrated features introduce a new technical solution for smart logistic items and intelligent transportation systems. In parallel, a management system, WSN data Collection and Management System (WiSeCoMaSys), is designed to interact with the deployed Wireless Sensor Networks. This tool allows the user to easily manipulate the sensor networks remotely. With its rich set of features such as real time data monitoring, data analysis and visualization, per-node management, and alerts, this tool helps both developers and users in the design and deployment of a sensor network. In addition, an analytical model is developed for comparison with the results from simulations and experiments. Focusing on the use of probability theory to model the network links, this model considers several important factors such as packet reception rate and network traffic which are used in the simulation and experiment parts. Moreover, the comparison between simulation, experiment and analytical results is also carried out to estimate the accuracy of the design and make several improvements of the simulation accuracy. Finally, all of the above parts are integrated in one unique system. This system is verified by both simulations in logistic scenarios (e.g., harbors, warehouses and containers) and experiments. The results show that the proposed model and protocol have a good packet delivery rate, little memory requirements and low delay. Accordingly, this system design is practical and applicable in logistics

Thermal Ignition by Vertical Cylinders

Accidental thermal ignition events present a significant hazard to the aviation industry. There is scarcity of experimental data on ignition by external natural convection flows for surface areas larger than 10 cm². In this work, thermal ignition of external natural convection flows by vertical cylinders is investigated. The effect of geometry is studied by resistively heating stainless steel cylinders of various sizes in a stoichiometric n-hexane and air mixture at 298 K and 1 bar. Cylinder lengths range from 12.7 to 25.4 cm, and cylinder surface areas vary from 25 to 200 cm². Logistic regression is used to provide statistical information about the ignition threshold (50% probability of ignition). The maximum ignition threshold found is 1117 K for a cylinder 12.7 cm long and 50 cm² in surface area. The minimum ignition threshold found is 1019 K for a cylinder 25.4 cm long and 200 cm² in surface area. The maximum uncertainty on these ignition thresholds is ±29 K, which comes from the maximum uncertainty on the pyrometer measurement used to record cylinder surface temperatures. The dependence of ignition threshold on both surface area and length of a cylinder is found to be minor. High speed visualizations of ignition indicated that ignition occurs near the top edge of all cylinders. The entire experimental setup is heated to allow for ignition tests with multi-component, heavy-hydrocarbon fuels including Jet A and two surrogate fuels, Aachen and JI. The cylinder used for all testing of heavier fuels is 25.4 cm long and 200 cm² in surface area. Hexane is also tested with the heated vessel to investigate the effect of ambient temperature on ignition. At an ambient temperature of 393 K, the ignition threshold of hexane is 933 K. Aachen has an ignition threshold of 947 K at an ambient temperature of 373 K. JI has an ignition temperature of 984 K at an ambient temperature of 393 K. Jet A has an ignition temperature of 971 K at an ambient temperature of 333 K. The maximum uncertainty on these thresholds is ±29 K. JI is found to be the most appropriate surrogate for Jet A. From the experiments, two main conclusions are reached. Ignition threshold temperatures in external natural convection flows are very weakly correlated with surface area. The observed ignition thresholds do not show the drastic transition of ignition temperature with surface area that is observed in internal natural convection situations. Observed ignition thresholds for comparable surface areas (100 to 200 cm²) are 500 to 600 K higher for external natural convection than internal natural convection. Hexane was found to be a reasonable surrogate for Jet A (38 K difference in ignition threshold) in external natural convection ignition testing. The more complex multi-component JI surrogate, while having an ignition threshold more comparable to Jet A (13 K difference in ignition threshold), requires heating the experimental apparatus and associated difficulties of fuel handling as well as the soot generation by combustion. Two simplified models of ignition are explored. The first is an investigation of ignition chemistry using a zero-dimensional reactor and a detailed kinetic mechanism for hexane. The temperature history of the reactor is prescribed by an artificial streamline whose rate of temperature increase is parametrically varied. The results from the zero-dimensional reactor computation reveal that a gradually heated streamline exhibits two-stage ignition behavior, while a rapidly heated streamline only experiences one ignition event. The second model of ignition is a one-dimensional simulation of ignition adjacent to a cylinder at a prescribed temperature. The formulation included diffusion of species and thermal energy as well as chemical reaction and employed Lagrangian coordinates. The chemistry is modeled with a reaction mechanism for hydrogen to reduce numerical demand. Heat flux and energy balance are analysed to gain insight into the ignition dynamics. Initially, heat transfer is from the wall into the gas, and a mostly nonreactive thermal boundary layer develops around the cylinder. As reaction in the gas near the surface begins to release energy, the heat transfer decreases, and, near the critical temperature for ignition, the direction of heat flux reverses and is from the gas into the wall. In a case where ignition takes place, there is rapid rise in temperature in the gas within the thermal layer, and a propagating flame is observed to emerge into surrounding cold gas. The heat transfer from the hot combustion products results in a continuous heat flux from the gas into the wall. In a case where ignition does not take place, no flame is observed and the heat flux at the wall is slightly positive. For the critical condition just below the ignition threshold, a balance between energy release and diffusion in the adjacent gas results in a small temperature rise in the thermal layer, but a propagating flame is not created. The Van't Hoff ignition criterion of vanishing heat flux at the ignition threshold is approximately but not exactly satisfied. Contrasting the two modeling ideas, we observe that modeling adiabatic flows along computed nonreactive streamlines is useful in examining the role of detailed chemistry but lacks important diffusion effects. Including mass and thermal transport provides more insight into important ignition dynamics but comes at the expense of increased computational complexity.</p