River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Special Topics in Structural Dynamics & Experimental Techniques, Volume 5 David S. Epp Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021 River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman, Ph.D. Society for Experimental Mechanics, Inc., Bethel, CT, USA
The Conference Proceedings of the Society for Experimental Mechanics Series presents early findings and case studies from a wide range of fundamental and applied work across the broad range of fields that comprise Experimental Mechanics. Series volumes follow the principle tracks or focus topics featured in each of the Society’s two annual conferences: IMAC, A Conference and Exposition on Structural Dynamics, and the Society’s Annual Conference & Exposition and will address critical areas of interest to researchers and design engineers working in all areas of Structural Dynamics, Solid Mechanics and Materials Research
River Publishers Special Topics in Structural Dynamics & Experimental Techniques, Volume 5 Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021 David S. Epp Editor
Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-4380-015-6 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Preface Special Topics in Structural Dynamics & Experimental Techniques represents one of nine volumes of technical papers presented at the thirty-ninth IMAC, A Conference and Exposition on Structural Dynamics, organized by the Society for Experimental Mechanics, and held between February 8 and 11, 2021. The full proceedings also include volumes on nonlinear structures and systems; dynamics of civil structures; model validation and uncertainty quantification; dynamic substructures; rotating machinery, optical methods, and scanning ldv methods; sensors and instrumentation, aircraft/aerospace, energy harvesting, and dynamic environments testing; topics in modal analysis and parameter identification; and data science in engineering. Each collection presents early findings from experimental and computational investigations on an important area within structural dynamics. Special Topics in Structural Dynamics & Experimental Techniques represents papers highlighting new advances and enabling technologies for experimental techniques, finite element techniques, system identification, and additive manufacturing. The organizers would like to thank the authors, presenters, session organizers, and session chairs for their participation in this track. Albuquerque, NM, USA David S. Epp v
Contents 1 A Comparative Study of Joint Modeling Methods and Analysis of Fasteners ............................ 1 Ricardo Garcia, Michael Ross, Benjamin Pacini, and Daniel Roettgen 2 Historical Perspective of the Development of Digital Twins................................................. 15 Matthew S. Bonney and David Wagg 3 Distributed Home Labs at the Time of the Covid ............................................................ 21 A. Cigada and S. Manzoni 4 Closed-Form Solutions for the Equations of Motion of the Heavy Symmetrical Top with One Point Fixed........................................................................................................ 29 Hector Laos 5 Equations of Motion for the Vertical Rigid-Body Rotor: Linear and Nonlinear Cases .................. 39 Hector Laos 6 Vibration Control in Meta-Structures Using Reinforcement Learning.................................... 55 D. Mehta and Vijaya V. N. Sriram Malladi 7 Using Steady-State Ultrasonic Direct-Part Measurements for Defect Detection in Additively Manufactured Metal Parts...................................................................................... 59 Erica M. Jacobson, Ian T. Cummings, Peter H. Fickenwirth, Eric B. Flynn, and Adam J. Wachtor 8 Toward Developing Arrays of Active Artificial Hair Cells .................................................. 75 Sheyda Davaria and Pablo A. Tarazaga 9 Challenges Associated with In Situ Calibration of Load Cells in Force-Limited Vibration Testing.... 81 Kenneth J. Pederson, Vicente J. Suarez, Emma L. Pierson, Kim D. Otten, James C. Akers, and James P. Winkel vii
Chapter 1 A Comparative Study of Joint Modeling Methods and Analysis of Fasteners Ricardo Garcia, Michael Ross, Benjamin Pacini, and Daniel Roettgen Abstract One of the more crucial aspects of any mechanical design is the joining methodology of parts. During structural dynamic environments, the ability to analyze the joint and fasteners in a system for structural integrity is fundamental, especially early in a system design during design trade studies. Different modeling representations of fasteners include spring, beam, and solid elements. In this work, we compare the various methods for a linear system to help the analyst decide which method is appropriate for a design study. Ultimately, if stresses of the parts being connected are of interest, then we recommend the use of the Ring Method for modeling the joint. If the structural integrity of the fastener is of interest, then we recommend the Spring Method. Keywords Finite element modeling · Joint modeling · Fasteners · Structural dynamics Nomenclature FEM Finite element method 1.1 Introduction One of the key components of any system in a structural dynamics analysis is the joints of the system. This work explores different techniques for modeling the joint system that use fasteners for linear models. There are several studies regarding the best methods to model these types of joints. Most of the research work attempts to address the nonlinearities in the system [1] caused by the joint. To be accurately predictive, it is important to eventually capture the nonlinearities. However, this work attempts to explore typical methods of modeling the joint in large structural dynamic system models, where one cannot computationally afford a high-fidelity model at the joint. These linear models are well suited for design studies and development of component specifications early on in a system’s initial design developments. During design studies, it is imperative that the analyst can generate several quick models of design parameters that can be assessed for structural dynamical performances. These structural performances can range from an assessment of the structural integrity of the parts and the fasteners to the motion of parts of the system to avoid impacts. During the design studies, the analyst is often faced with various methods of modeling the fastener. The analyst is often not afforded the time for deep study on the various methods of joining the materials. Consequently, this work explores various methods for one particular lap joint with fasteners. There are two typical concerns during design studies for the fastener. The first is the structural integrity of the parts being joined, and the second is the structural integrity of the fasteners and nut or insert. Stresses in the parts of interest are required to assess the structural integrity. However, some typical methods used for modeling the joints introduce stress singularities in the parts due to the use of rigid elements. This can lead to reporting incorrect stresses, especially as one appropriately refines the mesh. Hence, this work ultimately recommends using a method that assures proper reporting of the stress and can report the structural integrity of the fastener. R. Garcia · M. Ross ( ) · B. Pacini · D. Roettgen Sandia National Laboratories, Albuquerque, NM, USA e-mail: mross@sandia.gov © The Society for Experimental Mechanics, Inc. 2022 D. S. Epp (ed.), Special Topics in Structural Dynamics & Experimental Techniques, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-75914-8_1 1
2 R. Garcia et al. 1.2 Modeling Methods for Fastener Joints There are several methods for modeling fastener joints, see Fig. 1.1. Here we compare some common methods with the proposed method (Ring Method). The methods we explore are the following: 1. Tied surfaces at joint (Tied Contact Method) 2. Spring model of fastener (Spring Method) 3. Beam model of fastener (Beam Method) 4. Solid model of fastener (Plug Method) 5. Cylinder of solid elements (Ring Method) 6. Including preload and fastener properties (Ring-Beam Method) 1.2.1 Tied Surfaces at Joint: Tied Contact Method A straightforward method is to ignore the fastener and simply constrain the surfaces at the joint interface to move together. This removes the ability to do any post processing of the fastener itself. However, it is a typical method when the joint is not in an area of concern. In finite element terminology, this is typically referred to as “tied surfaces,” “glued surfaces,” or “tied contact.” Tying the surfaces at the joint together in this study is referred to as the Tied Contact Method. 1.2.2 Spring Model of Fastener: Spring Method In this technique, a spring element is used to connect the mating surfaces at the fastener shaft area and is the representation of the fastener. Rigid elements are used to connect one end of the spring element to the fastener location in one of the joining materials. A similar procedure is used for the other joining material. This is all depicted in Fig. 1.2. The fastener is not modeled with solid elements but represented with the spring element. If weight of the fastener is of a concern, concentrated masses can be added to the nodes of the spring element to account for the mass. This method is referred to as the Spring Method in this study. Fig. 1.1 Bolt modeling representations used in study
1 A Comparative Study of Joint Modeling Methods and Analysis of Fasteners 3 Fig. 1.2 Spring Method for representing fastener Fig. 1.3 Beam Method for representing fastener 1.2.3 Beam Model of Fastener: Beam Method Another common method for modeling the fastener joint for structural dynamics applications is the use of beam elements in place of the fastener. Typically, the beam is discretized to at least four to five elements to allow for preload application into one of the elements. Enough elements are also needed to capture the bending stiffness. A contact zone or connected surfaces can be represented at the interface of the joint from Shigley’s contact pressure frustrum formula [2]. This is depicted in Fig. 1.3. The fastener is not modeled with solid elements but represented with the beam elements. In this method, preload can or does not have to be considered. In this study, we compare a beam with preload referred to as the Beam Method. Preload is found as [3]: Fi = T Kt dbolt , (1.1) where T is the torque, Kt is the torque coefficient, anddbolt is the bolt diameter. The torque coefficient, Kt, also known as the nut factor, is a factor applied to account for the effects of friction. Typically, the torque coefficient for UNS Standard threads with coefficients of friction at 0.15 is 0.22 [4]. Calculating the forces to apply to the middle beam, see Fig. 1.3, is an iterative process to assure the correct force in the beams.
4 R. Garcia et al. Fig. 1.4 Plug Method for representing fastener 1.2.4 Solid Model of Fastener: Plug Method It is also common to see the fastener in a finite element model (FEM) to be represented with solid elements. In full system FEM that can have millions of elements, the threads are typically not modeled and are defeatured. The nut and head of the fastener are also defeatured and represented with cylinders. Including the washer is generally dictated by the analysis being conducted and the level of concern for the stress/strain near the fastener. Determining what is in contact or connected surfaces can also vary among analysts. We recommended using the contact zones shown in Fig. 1.4. In this study, we refer to this method as the Plug Method, since the solid fastener resembles a plug in the finite element model. Preload can be applied to a portion of the fastener shank. This is commonly introduced with a thermal strain on a portion of the solid elements representing the shank of the fastener, see Fig. 1.4. By knowing the desired preload force from Eq. (1.1) and the area of the shank, the desired stress in the shank can be determined and used for the iteration to find the appropriate thermal strain to get the correct preload. 1.2.5 Cylinder of Solid Elements: Ring Method The first two methods discussed, using spring or beam and rigid bar elements, Sects. 1.2.2 and 1.2.3, can potentially lead to erroneous stress predictions due to stress singularities. Though there are common methods to avoid reporting incorrect stresses in these cases, it is rather time consuming and difficult to automate. A simple method around this is to generate a cylinder of solid elements. Shigley’s formula for calculating the frustum can be used for determining the radius of the cylinder. In this study, the Ring Method is explored (Fig. 1.5). 1.2.6 Including Preload and Fastener Properties: Ring-Beam Method It is possible to include this technique with the previous mentioned methods. If it is desired to include a preload or obtain fastener forces, one can use this method in conjunction with the Beam Method, Sect. 1.2.3. This allows for obtaining the fastener loads for analysis. When reporting the stress in the joining parts, the analyst can easily remove the ring part that would have the stress singularities due to the rigid elements for the beam. This method is referred to as the Ring-Beam Method (Fig. 1.6).
1 A Comparative Study of Joint Modeling Methods and Analysis of Fasteners 5 Fig. 1.5 Ring Method for representing fastener Fig. 1.6 Ring Method with beam for preload or obtaining fastener forces Fig. 1.7 Shigley’s frustum calculation [2] 1.2.7 Frustrum Calculation The method recommended for finding the geometry of the frustrum is that by Shigley [2]. In this method, the stiffness in a layer is obtained by assuming the stress field looks like a frustum of a hollow cone, see Fig. 1.7. Shigley recommends an angle, α of 30◦, where the angle is typically between 25 and 33 degrees.
6 R. Garcia et al. 1.3 Example Problem An example problem is used in this study to demonstrate the applicability of the different methods. It is represented as a cylinder with a plate at one end and a beam on top of the plate, see Fig. 1.8. There are eight ¼-20 fasteners used to connect the plate to the cylinder. The fastener properties used are those of steel. For this study, the fastener models were made to be very stiff in the attempt of obtaining stiffness values on the order of 1.0 ×107 lb/in. The plate, cylinder, and rectangular beam are aluminum. The photos shown in Fig. 1.9 are representative of the test model. Fig. 1.8 Cylinder-plate-beam example with fasteners connecting plate to cylinder Fig. 1.9 Test model photos
1 A Comparative Study of Joint Modeling Methods and Analysis of Fasteners 7 Modal Shaker Input Fig. 1.10 Modal shaker input Accelerometers Fig. 1.11 Accelerometer locations used in study There were two experiments conducted. The first was a free boundary condition modal experiment. The second experiment performed was a burst random excitation at the base of the cylinder with the force applied in the Y-direction, as shown in Fig. 1.10. The burst random excitation signal was signal processed and removed the off times to provide an ergodic, stationary random signal. There are 28 attached triaxial accelerometers used in the experiment. However, this study focused on five triaxial accelerometers that were surrounding one of the fasteners as shown in Fig. 1.11. Figure 1.12 depicts the specific accelerometer gage number noted in this study. There are three gages noted as aft that are on the excitation side of the joint. There are two gages on the forward end of the joint near the beam. The forward/aft designation is from missile terminology, where the shaker and beam represent the rocket motors and the missile payload, respectively. 1.4 Results 1.4.1 Modal Comparisons The first comparison of the methods is a modal analysis. The modal analysis for a free boundary condition is shown in Table 1.1 with the first six modes being rigid body. In the modal analyses, the initial model (Tied Contact Method) was correlated to the test data by a previous analyst. Recall that the model for the Tied Contact Method was developed with surfaces at the joints constrained by multipoint constraints typically referred to as tied surfaces or glued surfaces. Then, the other models were developed with no tuning of the fastener method. The idea was to generate the methods as if no test data was available and see which performed the most accurate. As indicated in Table 1.1, the mode frequencies were insensitive to the modeling method used. The error percentage difference of each method compared to the test is shown Fig. 1.13. Generally, the largest error was noted at modes 11 and 15,
8 R. Garcia et al. (A) Aft Left Gage (B) Aft Center Gage (C) Aft Right Gage (D) Forward Left Gage (E) Forward Center Gage 3180 3498 6585 47564 47594 Fig. 1.12 Specific accelerometer gages Table 1.1 Modal frequency (Hz) comparison between test and simulation Mode Test data Tied contact Plug Ring Ring-beam Spring Beam 7 139 141 141 141 139 142 139 8 182 182 182 183 180 185 180 9 385 398 398 398 393 399 393 10 390 398 398 398 398 399 398 11 590 543 543 551 544 568 551 12 945 948 948 948 949 949 949 13 951 948 948 948 952 949 952 14 1039 1045 1045 1046 1030 1047 1031 15 1221 1323 1323 1322 1293 1325 1293 16 1288 1323 1323 1322 1320 1325 1320 which are an axial and ovaling mode of the system, respectively. This may be a question of material properties as opposed to fastener issues. 1.4.2 Random Vibration Comparisons A typical study will require a random vibration analysis of the system for structural dynamics performance. In this regard, we compare accelerometer responses on two sides of the joint and see if there is any clear indication of a preferred modeling method for the fastener. The acceleration responses are noted in the auto-spectral densities shown in Figs. 1.14, 1.15, 1.16, and 1.17, where the X-direction is transverse and the Y-direction is axial. The responses were grouped into similar behaving responses with the Beam, the Plug, and the Tied Contact methods grouped together and shown in the right column of Figs. 1.14, 1.15, 1.16, and 1.17. This leaves the Spring, the Ring, and the Ring-Beammethods in the other group and shown in the left column of Figs. 1.14, 1.15, 1.16, and 1.17. In this particular experiment, the Springand the Ringmethods have responses that are similar and appear to be more accurate than the Beam, Plug, and Tied Contact methods. The Spring and Ring methods also lend themselves to easier implementation over the previous methods. Any of the methods, however, appear to be adequate and could benefit from furthering calibration.
1 A Comparative Study of Joint Modeling Methods and Analysis of Fasteners 9 Fig. 1.13 Percent difference between test data and various methods for modal analysis None of the methods do a particular good job of capturing the response at the forward center location, Fig. 1.17. This is an area of future study and probably due to nonlinear issues. 1.5 Conclusion This paper explores various methods of modeling fasteners. The hope is that it can provide the analyst with a method that is consistent with reporting stresses in the parts being joined and providing the fastener loads. Under this specific lap joint, it is recommended to use the Ring Method. It is suggested, however, to use the Spring Method if the structural integrity of the fastener is of interest. The Ring-Beam Method would be suitable if preload and stress near the fastener is of concern. It is beneficial that the Ring, the Ring-Beam, and the Spring methods are easily implemented. Any of the methods, however, appear adequate and could profit from furthering calibration. Future work should explore additional joints as well as the response at the forward center fastener gage location where none of the methods did particularly well at matching that response.
10 R. Garcia et al. Fig. 1.14 X-direction responses aft of bolted joint compared to test
1 A Comparative Study of Joint Modeling Methods and Analysis of Fasteners 11 Fig. 1.15 X-direction responses forward of bolted joint compared to test
12 R. Garcia et al. Fig. 1.16 Y-direction responses aft of bolted joint compared to test
1 A Comparative Study of Joint Modeling Methods and Analysis of Fasteners 13 Fig. 1.17 Y-direction responses forward of bolted joint compared to test Acknowledgments Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy National Nuclear Security Administration under contract DE-NA0003525. SAND2020-13563C. References 1. Brake, M.R. (ed.): The Mechanics of Jointed Structures: Recent Research and Open Challenges for Developing Predictive Models for Structural Dynamics. Springer, Cham (2018) 2. Budynas, R.G., Nisbett, J.K.: Shigley’s: Mechanical Engineering Design, 9th edn. McGraw-Hill Publishing Co., New York (2012) 3. Chambers, J.: Preloaded Joint Analysis Methodology for Space Flight Systems, Technical Report 106943, NASA (1995) 4. Norton, R.: Machine Design: an Integrated Approach. Pearson Prentice Hall, New Jersey (1998)
Chapter 2 Historical Perspective of the Development of Digital Twins Matthew S. Bonney and David Wagg Abstract With modern advances in high-performance computing, design engineers have put a large focus on digital testing and simulations to inform new systems. In addition, recent market tendencies show a desire to reduce waste and for longer designed life. One major strategy used to meet these trends is the utilization of a digital twin. Digital twins are numerical analogues to physical systems such as aircraft, auto-mobiles, and power generation systems. With the wide applicability of the digital twin, an understanding of their development can give insight into the impact and direction of recent research. Understanding these advancements can also give confidence in both the technique of using a digital twin and the simulated predictions to various loading conditions. This chapter focuses on detailing the historical development of digital twins to the state-of-the-art research being done and specifically how it is relevant to the structural dynamics community. 2.1 Background Using computational models to simulate physical phenomena is by no means novel. Recently, however, there has been an increase in desire to integrate the computational models into the design process. Additionally, there is an increased need to expand the models to be accurate for the life cycle of a system. This is where the concept of twinning, especially digital twins, originates and the main motivation of recent research. The discussion of integrating a twin into designs dates back to NASA’s Apollo mission [1]. The twin for the NASA Apollo mission incorporated a physical cockpit to use during training and diagnostic testing. The nomenclature of digital twin is based on the work in product life-cycle management [2]. This was first published in the ASME Standard for Verification and Validation (V&V) in Computational Solid Mechanics (ASME V&V 10) [3]. In the ASME standard, a digital twin is defined as “Digital Twin is an integrated multiphysics, multiscale simulation of a vehicle or system that uses the best available physical models, sensor updates, fleet history, etc., to mirror the life of its corresponding flying twin.” A common generalization of this definition is the use of the term physical twin instead of flying twin to incorporate non-aerospace systems. From this definition, there are a few main aspects, first being the multiphysics and multiscale simulations. The majority of the digital twins incorporate multiphysics, such as structural and fluid dynamics (such as aerodynamic pressures on an aircraft during flight). Using multiscale simulations, however, seems to be more flexible depending on the physical twin. For industrial systems, the multiscale aspects are typically included; however, academic systems do not tend to have multiscale since they can be designed to only contain a single length scale of importance. A second aspect of this definition is the incorporation of “physical models, sensor updates and fleet history.” This included model updating, grey-box modeling (combination of computational models and sensor data), and pure sensor-based models. The last aspect is the ability to “mirror the life of the flying twin.” Around the same time as the ASME standard was published, several other terms have been used to describe identical or similar ideas. For example, Digital Counterpart [4], Virtual Engine [5], Intelligent Prognostic Tools [6], and Mirrors [7] to mention a few. Many of these alternative names tend to focus on either a specific type of physics (electrical or hydraulic, for example), scale, or specifying computational/sensor-based models only. The term digital twin captures the underlying meaning for these systems and allows for a better understanding for a general audience. This chapter discusses some usages of the digital twins and describes different types of digital twins. Section 2.2.1 discusses how digital twins are used in the design of a new system, and Sect. 2.2.2 discusses the utilization during the M. S. Bonney ( ) · D.Wagg Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Sheffield, UK e-mail: david.wagg@sheffield.ac.uk © The Society for Experimental Mechanics, Inc. 2022 D. S. Epp (ed.), Special Topics in Structural Dynamics & Experimental Techniques, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-75914-8_2 15
16 M. S. Bonney and D. Wagg manufacturing process. In Sect. 2.3, discussion is held on how the digital twin is utilized to determine the life cycle and how it can be used for Verification, Validation, and Uncertainty Quantification (VVUQ). Finally, Sect. 2.4 discusses the different types of digital twins via a hierarchy with some concluding remarks in Sect. 2.5. 2.2 Pre-delivery Usage Currently, one of the major uses of a digital twin is based on the design/prototyping stages of a system. This is primarily due to the required time to see a system from design to decommission. Systems such as aircraft can have life spans that last for nearly 30 years. This creates a large time lag between modern digital twins and the complete validation over the entire life cycle. 2.2.1 Design Usage One of the major uses of a digital twin is to aid in the design and prototyping of a new system. This is particularly true for high-consequence systems that are sparsely manufactured such as aerospace or nuclear systems. One of the primary steps in the design process is the use of Computer-Aided Design (CAD) to create and test candidate designs. Particularly, a digital twin can help for design modifications [8] or long-term failure criteria [9]. In addition to CAD, digital twins also help aid in the prototype stages of the design. However, utilizing the data from prototype tests leads to an issue with how to incorporate this large amount of information, aka big data, into a digital twin and how an analyst visualizes the results. A large amount of research is being done in the field of big data [10, 11] and utilizing the Internet of Things [12, 13]. Another interesting aspect of using digital twins is the ability to incorporate data and models from various sources. One example of this is in the use of electronics that use a digital twin to incorporate a block chain methodology [14]. 2.2.2 Manufacturing Usage An initial explanation of digital twins might give the impression that it is only useful for design and long-term monitoring; this however is not true. Digital twins can aid in the manufacturing process and enable modern research techniques. One use of digital twins is based on the ability to utilize sensor data and incorporate live data. Modern manufacturing utilizes a large amount of sensors for both the machinist and the manufacturer for quality control. The utilization of these sensors during manufacturing is called real-time manufacturing [15]. One main aspect that a digital twin can be used is in the use of CNC automated manufacturing. The digital twin allows for the transfer of information between design, purchasing, and manufacturing that can minimize the time between ordering and receiving a product [1]. Additionally, utilizing digital twins also increases the traceability of any issues and can account for any maintenance or other issues [16]. In addition to CNC, digital twins can also be greatly helpful for Additive Manufacturing (AM). In order to manufacture via AM, a specific path must be simulation and verified that the structure meets design requirements. A digital twin can utilize these path simulations both for verification and for design modifications [17, 18]. 2.3 Asset Management Usage One major use of the digital twin involves the incorporation of full life-cycle monitoring and modeling. The advancements discussed in Sect. 2.2 are expansions of other current research by the utilization and centralization of sensors, simulations, and historical data. However, one of the major utilizations of the digital twin is the mirroring of scenarios to the physical twin. This section discusses how the digital twin can be used in the delivery and maintenance for the life span of the product.
2 Historical Perspective of the Development of Digital Twins 17 2.3.1 Life-Cycle Determination One of the advantages for using a digital twin is the ability to take long-term measurements and perform simulations to predict how the system changes during the time in operation. This ability to perform during the operation allows for both monitoring and predicting damage/failure. One aspect of this is the maintenance and intelligent prognosis [6]. The concept of intelligent prognosis is an interesting combination of monitoring data and future predictions. In [6], the authors utilize the Watchdog AgentTM to take in monitoring data and make updated predictions on the system. Another aspect of the digital twin is the one-to-one relationship between the digital and physical twins. This allows for models to use an accurate model for the specific system, including the manufacturing defects. The termas-manufactured geometry is commonly used to describe the physical system as opposed to the nominal geometry that does not account for manufacturing tolerances that can create issues particularly for nonlinear systems [19]. This is also important for the study of how manufacturing and assembly uncertainty affect the life span of a system and help identify required maintenance for the physical twin. In addition to predictions based on normal operation, the digital twin can also aid in the identification of damage through structural health monitoring (SHM). This is especially important for systems with long expected life, such as space vehicles [20], civil structures, and aircraft. While the work in [20] performs damage detection with no modeling, this type of work can be expanded to utilize the damage information into the digital twin and possibly make future predictions, such as in [21]. 2.3.2 VVUQ The study of VVUQ with digital twins participates in two main aspects: model updating and uncertainty quantification. Model updating is not novel to digital twins as it has been a major part of structural dynamic modeling [22]. However, the advancements in model updating, particularly in nonlinear dynamics [23, 24], can easily be modified to utilize the wealth of information contained within a digital twin. One particularly interesting aspect of model updating is utilizing the associated sensors available to the digital twin. This includes the ability to perform tests periodically during the system’s operation. Two methods to incorporate these sensors for model updating are Bayesian networks [25] and Bayesian operational modal analysis [26]. In addition to model updating, the quantification of uncertainty, both physical and numerical, is also an important aspect of the digital twin [27, 28]. For digital twins, there are several sources of uncertainty including: • Sensor Uncertainty: All the sensors are calibrated to a specified tolerance based on calibration standards. Additionally, the location of sensor has physical dimensions that are not typically explicitly modeled. • Manufacturing/Assembly Uncertainty: Manufacturing parts is not perfectly exact but is specified within a certain range (typically very small). These ranges can build up and potentially cause discrepancy between the model and the physical twin. For digital twins that correspond to a singular physical system, this uncertainty is nearly zero, but can be larger is a digital twin is used to express more than one physical twin (such as specific aircraft model). • Averaging Error: Since the digital twin is used for the entire life expectancy of the system, parameters (such as stiffness) can change over time due to damage or degradation. Snapshot-based calculations can ignore the history of the parameters, but aspects such as predictions need to incorporate all the historical data. This error is associated with any averaging that is used incorporating data collected from multiple sources or instances. • Model-Form Uncertainty: It is very unlikely that the entirety of the experienced physics is modeled. However, very accurate approximations are used (such as finite elements). This uncertainty accounts for the physical to numerical errors and other assumptions made (linear vibrations, rigid connections, etc.) in the computational models. 2.4 Digital Twin Hierarchy As one can surmise from the history and discussion of digital twins so far in this chapter, digital twins are complicated systems. To better categorize the aspects of digital twins, the authors in [29] introduce a hierarchical view of the technology that is utilized in digital twins. This hierarchy is presented in Fig. 2.1 with increasing complexity and technology evolution closer to the tip of the pyramid.
18 M. S. Bonney and D. Wagg Fig. 2.1 Hierarchy organization of digital twins (taken from [29]) It is important to note that aspects of the digital twin are evolutions of conditional monitoring of plants such as those used for power generation. As a basic need, the ability to supervise is the first desirable aim. The ability to monitor the operations of systems is vital. A second basic need is the ability to manipulate operations based on the data recorded (such as environmental temperature and space availability). These aspects make up the first two levels of a digital twin with level one being Supervisory, the ability to monitor the system, and level two being Operational, the ability to make operational decisions based on the data recorded from the monitor data. The first two levels are very well established. Some authors have considered this a digital twin; however, modern interpretations classify these two levels as predigital twins, meaning that they have the capacity of becoming a digital twin but do not contain all the necessary abilities needed for a digital twin. The next level of sophistication is the incorporation of simulations to make predictions on the system. At this level, the authors in [27] utilize the name simulation digital twin. This builds on the supervisory and operational capacity of the predigital twin and incorporates numerical simulations to compute data that is not directly observed on the system. The inclusion of numerical simulations also gives the user a graphical interface to utilize. Simulation digital twins can both give predictions (such as maximum stress during normal operation) and a quantitative measure of the trust for predictions through the use of uncertainty quantification. This level is the current level of most digital twins. With the current evolution of digital twins residing primarily in level three, there are two more levels of advancements that are aspirations for digital twin sophistication. The first level of advancement is the introduction of intelligence through learning. This level introduces the concept of learning from data (via machine learning) and adds levels of scenario planning and decision support. The final level allows the digital twin to perform autonomously. Adding this level allows for the digital twin to perform routine decision-making, within specified ranges, without requiring a user decision. One simple example of this level would be to have an automatic climate control within a structure (such as a space system) that takes in temperature/humidity measurements, simulate what vents would provide the most efficient climate control, and to automatically turn on the heater/cooler and open the required vents. This hierarchy view of digital twins gives an understanding on what baseline information/developments are needed for the development of digital twins. The aspiration of intelligent/autonomous digital twins is currently a large focus of current research. Additionally, advancement in model simulations can also greatly advance aspects of digital twins. These are generally viewed as making the digital twin more accurate, perform simulations with less computational burden, or better incorporate the operational data into the simulations and decision-making. 2.5 Conclusions Despite being a modern buzz word, digital twins have a rich historical aspect to them. They date back to NASA’s Apollo mission as a method to monitor and simulate product life-cycle management and aid in personnel training. The evolution
2 Historical Perspective of the Development of Digital Twins 19 of digital twins is comprised of multiple layers involving experimental testing, numerical modeling, product life-cycle monitoring, and decision-making. There are two main time spans of interest for digital twins, pre-delivery, and asset management. The time span of predelivery is focused from the initial design phase until the product is delivered to the customer. For an initial design, digital twins aid in the general design by aiding the ability to make design modifications informed by simulating the failure criteria. Additionally, a digital twin can be very useful during the prototyping stage with data management, grey-box modeling, and model updating. After the delivery of the product to the customer, the digital twin is also very useful in the long-term monitoring and modeling of the system. To ensure that a digital twin corresponds nearly perfectly to the physical twin, a large amount of model verification, validation, and uncertainty quantification is performed. This can also be used to identify long-term aspects such as maintenance and monitoring using the data from structural health monitoring. Digital twins are still an evolving and expanding area of research. To better characterize the development process and the wide possibility of digital twins, a five-level hierarchy from various sources is examined to better understand the state-ofthe-art development and the possibilities available for future research. The development of digital twins is ongoing but still has an interesting history. References 1. Rosen, R., von Wichert, G., Lo, G., Bettenhausen, K.D.: About the importance of autonomy and digital twins for the future of manufacturing. IFAC-PapersOnLine 48(3), 567–572 (2015). 15th IFAC Symposium on Information Control Problems in Manufacturing 2. Grieves, M., Vickers, J.: Digital Twin: Mitigating Unpredictable, Undesirable Emergent Behavior in Complex Systems, pp. 85–113. Springer International Publishing, Cham (2017) 3. Schwer, L.E.: An overview of the ASME v&v-10 guide for verification and validation in computational solid mechanics. In: 20th International Conference on Structural Mechanics in Reactor Technology, pp. 1–10 (2009) 4. Nicolai, T., Resatsch, F., Michelis, D.; The web of augmented physical objects. In: International Conference on Mobile Business (ICMB’05), pp. 340–346 (2005) 5. Morel, T., Keribar, R., Leonard, A.: “Virtual engine/powertrain/vehicle” simulation tool solves complex interacting system issues. In: SAE Technical Paper. SAE International, 03 (2003) 6. Lee, J., Ni, J., Djurdjanovic, D., Qiu, H., Liao, H.: Intelligent prognostics tools and e-maintenance. Comput. Ind. 57(6), 476–489 (2006). E-maintenance Special Issue 7. Worden, K., Cross, E.J., Barthorpe, R.J., Wagg, D.J., Gardner, P.: On digital twins, mirrors, and virtualizations: frameworks for model verification and validation. ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg 6(3), 05, 030902 (2020) 8. Schleich, B., Anwer, N., Mathieu, L., Wartzack, S.: Shaping the digital twin for design and production engineering. CIRP Ann. 66(1), 141–144 (2017) 9. Boschert, S., Rosen, R.: Digital Twin—The Simulation Aspect, pp. 59–74. Springer International Publishing, Cham (2016) 10. Tao, F., Cheng, J., Qi, Q., Zhang, M., Zhang, H., Sui, F.: Digital twin-driven product design, manufacturing and service with big data. Int. J. Adv. Manufact. Technol. 94(9–12), 3563–3576 (2018) 11. Tao, F., Sui, F., Liu, A., Qi, Q., Zhang, M., Song, B., Guo, Z., Lu, S.C.-Y., Nee, A.Y.C.: Digital twin-driven product design framework. Int. J. Prod. Res. 57(12), 3935–3953 (2019) 12. Lee, J., Lapira, E., Bagheri, B., Kao, H.: Recent advances and trends in predictive manufacturing systems in big data environment. Manufact. Lett. 1(1), 38–41 (2013) 13. Schroeder, G.N., Steinmetz, C., Pereira, C.E., Espindola, D.B.: Digital twin data modeling with automationML and a communication methodology for data exchange. IFAC-PapersOnLine 49(30), 12–17 (2016). 4th IFAC Symposium on Telematics Applications TA 2016 14. Heber, D., Groll, M., et al.: Towards a digital twin: How the blockchain can foster e/e-traceability in consideration of model-based systems engineering. In: DS 87-3 Proceedings of the 21st International Conference on Engineering Design (ICED 17) Vol 3: Product, Services and Systems Design, Vancouver, 21–25.08. 2017, pp. 321–330 (2017) 15. Uhlemann, T.H.-J., Schock, C., Lehmann, C., Freiberger, S., Steinhilper, R.: The digital twin: demonstrating the potential of real time data acquisition in production systems. Procedia Manufact. 9, 113–120 (2017). 7th Conference on Learning Factories, CLF 2017 16. Ríos, J., Hernandez, J.C., Oliva, M., Mas, F.: Product avatar as digital counterpart of a physical individual product: Literature review and implications in an aircraft. In: ISPE CE, pp. 657–666 (2015) 17. Knapp, G.L., Mukherjee, T., Zuback, J.S., Wei, H.L., Palmer, T.A., De, A., DebRoy, T.: Building blocks for a digital twin of additive manufacturing. Acta Mat. 135, 390–399 (2017) 18. DebRoy, T., Zhang, W., Turner, J., Babu, S.S.: Building digital twins of 3d printing machines. Scripta Mat. 135, 119–124 (2017) 19. Cerrone, A., Hochhalter, J., Heber, G., Ingraffea, A.: On the effects of modeling as-manufactured geometry: toward digital twin. Int. J. Aerosp. Eng. 2014, 439278 (2014) 20. Zagrai, A., Doyle, D., Gigineishvili, V., Brown, J., Gardenier, H., Arritt, B.: Piezoelectric wafer active sensor structural health monitoring of space structures. J. Intell. Mat. Syst. Struct. 21(9), 921–940 (2010) 21. Seshadri, B.R., Krishnamurthy, T.: Structural health management of damaged aircraft structures using digital twin concept. In: 25th AIAA/AHS Adaptive Structures Conference, pp. 1675 (2017) 22. Friswell, M., Mottershead, J.E.: Finite Element Model Updating in Structural Dynamics, vol. 38. Springer Science & Business Media, Berlin (2013)
20 M. S. Bonney and D. Wagg 23. Worden, K., Wong, C.X., Parlitz, U., Hornstein, A., Engster, D., Tjahjowidodo, T., Al-Bender, F., Rizos, D.D., Fassois, S.D.: Identification of pre-sliding and sliding friction dynamics: grey box and black-box models. Mech. Syst. Signal Process. 21(1), 514–534 (2007) 24. Worden, K., Barthorpe, R.J., Cross, E.J., Dervilis, N., Holmes, G.R., Manson, G., Rogers, T.J.: On evolutionary system identification with applications to nonlinear benchmarks. Mech. Syst. Signal Process. 112, 194–232 (2018) 25. Li, C., Mahadevan, S., Ling, Y., Choze, S., Wang, L.: Dynamic Bayesian network for aircraft wing health monitoring digital twin. AIAA J. 55(3), 930–941 (2017) 26. Au, S.K., Zhang, F.L., Ni, Y.C.: Bayesian operational modal analysis: theory, computation, practice. Comput. Struct. 126, 3–14 (2013). Uncertainty Quantification in structural analysis and design: To commemorate Professor Gerhart I. Schueller for his life-time contribution in the area of computational stochastic mechanics 27. Tuegel, E.J., Ingraffea, A.R., Eason, T.G., Spottswood, S.M.: Reengineering aircraft structural life prediction using a digital twin. Int. J. Aerosp. Eng. 2011, 154798 (2011) 28. Karve, P.M., Guo, Y., Kapusuzoglu, B., Mahadevan, S., Haile, M.A.: Digital twin approach for damage-tolerant mission planning under uncertainty. Eng. Fract. Mech. 225, 106766 (2020) 29. Wagg, D.J., Worden, K., Barthorpe, R.J., Gardner, P.: Digital twins: state-of-the-art and future directions for modeling and simulation in engineering dynamics applications. ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg 6(3), 05, 030901 (2020)
Chapter 3 Distributed Home Labs at the Time of the Covid A. Cigada and S. Manzoni Abstract The well-known difficulties with the recent pandemic have forced people to find new communication means, especially concerning educational methods. University courses have been dramatically changed in their structure, just in a few weeks. While traditional lectures have been more easily switched to “on-line” methods and tools, classes mainly based on experimental lab activities have suffered more from the new forced approaches: a new and stronger effort had to be produced to guarantee the proper knowledge transfer. Many ways have been tried to export experimental labs into students’ houses, preserving and stimulating their curiosity. However, there was a risk to foster a more passive role; students watching a movie or listening to a faraway teacher could not have direct interaction with the instrumentation locked in not accessible labs, nor had the important chance to develop “hands-on” sessions. This paper deals with the ideas and attempts to preserve the value of the experimental activities during the COVID period, in which experimentation has also meant experimenting a new way of teaching; early attempts will be described up to a final proposal, which has been successfully tested with students of both the bachelor and the master of science. Keywords Smartphone · Educational laboratories 3.1 Introduction During the recent pandemic, it seemed that a real chance to perform experimental classes was completely lost. Students could not have access to the University classrooms, most of them had returned to their native countries: even if on-line teaching seemed to make the world smaller, some distances proved to be incredibly wider, as the personal contact and the possibility to interact with real instrumentation seemed unrecoverable. A proper problem introduction requires a short history related to the environment in which the project to get over the mentioned difficulties was born: this history relates to the situation of University studies, mainly in Mechanical Engineering, in Italy. Italy has a specific situation as, in University courses, Measurements are considered a discipline on its own. The advance of metrology issues and the complexity linked to a proper management of measurement systems and networks, together with the needed data management strategies, have led to consider a specific skill: the measurement specialist. This is the reason, especially in Mechanical Engineering, a long tradition exists in creating and managing experimental labs, to properly train students, since the bachelor courses. From the 1990s on, in many Italian universities an effort has been made not just in setting up experimental laboratories, but also to make them an effective educational tool, overcoming a series of barriers which leads to consider experimentation less important than modeling. Literature on this topic tends to focus on single experiments or tests, rather than working on a general method: one of the few examples in this direction is given by the works of the Portuguese group of Maria Teresa Restivo [1, 2]. A. Cigada ( ) · S. Manzoni Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy e-mail: alfredo.cigada@polimi.it © The Society for Experimental Mechanics, Inc. 2022 D. S. Epp (ed.), Special Topics in Structural Dynamics & Experimental Techniques, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-75914-8_3 21
22 A. Cigada and S. Manzoni 3.2 Experimental Laboratories as a Tool for Practitioner Engineering The first attempts to set up educational labs consisted in big rooms having desks equipped with the basic instrumentation: power supply, multimeter, frequency generator, data acquisition boards, and some sensors (Fig. 3.1). It was immediately recognized that the main effort was not just in setting up the lab, but in maintaining it. Maintenance was not just related to the relevant use of these facilities, creating wear and damage, but also to instrumentation aging and the need to substitute it. Safety issues had to be properly transferred to students working in the labs, instructors had to be trained: in the end all these aspects often made the choice of having experimental labs very expensive, sometimes not sustainable. Other issues were related to the need to provide quick instructions for the students, to help them learning how to use the instrumentation. This aspect required times not always available in courses, which need to run fast, usually around 3 months. The proposed experiments spanned across the whole world of measurements, every test having an introduction, some guided tests, and in the end some hints to develop some work on own, in which the instructor had the main role of a living manual. Particular care was devoted to the dynamic performances in measurements, being this the most tricky part in mechanical measurements: most examples, coming from the area of sound and vibrations, were modeled on the remarkable activity of Anders Brandt [3–7]. In the end, due to the usually high number of students attending courses, it is hardly possible to allow each individual to practice “hands-on sessions” as students usually work in small groups. The dynamics of social relations inside groups has to be carefully studied, as some students tend to hide themselves, not being very active, while others do most of the job, although in the end the single student activity has to be evaluated. In case we really wanted each single student to practice in person on the instrumentation, time and resources were not enough. This is the reason research on the best way to perform experimental activities in university classes never stopped. A first and almost immediate solution was trying to lower the high pressure on experimental labs, by transferring some activities into common classrooms. This was possible thanks to a joint initiative with National Instruments and PCB. The first company offered help in the use of a product, my-DAQ [8], which can be adapted to multiple uses, like a multimeter, a function generator, a spectrum analyzer, a data acquisition system, and many others, relying on virtual instrumentation developed on a computer with Labview [9]. PCB [10] offered some instrumentation out of production, still perfectly working, which could be used to work on simple experiments: they were microphones and accelerometers, giving many chances to develop small classroom projects, assuming that a table can pretend to be a bridge, fan coils are narrow band noise generator, a set of microphones can be used to get the speed of sound, and so on. In some specific cases, students could borrow the sensors for their tests, to be carried out on own: in one case, an archery champion asked to measure the bow vibrations while shooting an arrow, also getting interesting results to improve his performances. In addition, students had the chance to obtain a free of charge student edition of Labview; this solution was chosen because the Express VI family allows one to use the basic tools of data acquisition and spectral analysis even without being an expert in programming and in a very short time. The idea of having a laboratory easily transferrable everywhere was really challenging and effective in getting the goals of making lab activity easier and accessible to everyone: for this reason, this project was given a name: “Flying Lab” meaning the possibility of easily reach every place. But many problems were still not solved and a new revolution was starting. Fig. 3.1 The first educational laboratories in Politecnico di Milano (left); the “Flying Lab”: every classroom can become a lab
RkJQdWJsaXNoZXIy MTMzNzEzMQ==