scholarly journals Design of a Flexure Rotational Time Base with Varying Inertia

2021 ◽  
pp. 1-23
Author(s):  
Etienne Thalmann ◽  
Simon Henein
Keyword(s):  
Practical Method ◽  
Analytical Models ◽  
Elastic Behavior ◽  
Time Base ◽  
Proof Of Concept ◽  
Inertia Effects ◽  
Quartz Oscillator ◽  
Mems Oscillators ◽  
Nonlinear Elastic ◽  
Frequency Variations

Abstract Flexure oscillators are promising time bases thanks to their high quality factor and monolithic design compatible with microfabrication. In mechanical watchmaking, they could advantageously replace the traditional balance and hairspring oscillator, leading to improvements in timekeeping accuracy, autonomy and assembly. As MEMS oscillators, their performance can rival that of the well-established quartz oscillator. However, their inherent nonlinear elastic behavior can introduce a variation of their frequency with amplitude called isochronism defect, a major obstacle to accurate timekeeping in mechanical watches. Previous research has focused on addressing this issue by controlling the elastic properties of flexure oscillators. Yet, these oscillators exhibit other amplitude-related frequency variations caused by changes of inertia with amplitude. In this article, we not only improve existing models by taking into account inertia effects but also present a new way of using them to adjust the isochronism defect. This results in a better understanding of flexure oscillators and an alternative way of tuning isochronism by acting on inertia instead of stiffness. This also opens the door to new promising architectures such as the new Rotation-Dilation Coupled Oscillator (RDCO) whose symmetry has the advantage of minimizing the influence of linear accelerations on its frequency (the other major limitation of flexure oscillators). We derive analytical models for the isochronism of this oscillator, show a dimensioning with compensating inertia and stiffness variations and present a practical method for post-fabrication isochronism tuning. The models are validated by FEM and mock-ups serve as preliminary proof-of-concept.

scholarly journals Flexure Pivot Oscillator With Intrinsically Tuned Isochronism

2019 ◽  
Vol 142 (7) ◽  
Author(s):  
E. Thalmann ◽  
M. H. Kahrobaiyan ◽  
I. Vardi ◽  
S. Henein
Keyword(s):  
Oscillation Amplitude ◽  
Analytical Models ◽  
Essential Property ◽  
Proof Of Concept ◽  
Parasitic Motion ◽  
Element Simulation ◽  
Spiral Spring ◽  
Elastic Nonlinearity ◽  
The One ◽  
Nonlinear Elastic

Abstract The most important property for accurate mechanical time bases is isochronism: the independence of period from oscillation amplitude. This paper develops a new concept in isochronism adjustment for flexure-based watch oscillators. Flexure pivot oscillators, which would advantageously replace the traditional balance wheel-spiral spring oscillator used in mechanical watches due to their significantly lower friction, exhibit nonlinear elastic properties that introduce an isochronism defect. Rather than minimizing this defect, we are interested in controlling it to compensate for external defects such as the one introduced by escapements. We show that this can be done by deriving a formula that expresses the change of frequency of the oscillator with amplitude, i.e., isochronism defect, caused by elastic nonlinearity. To adjust the isochronism, we present a new method that takes advantage of the second-order parasitic motion of flexures and embody it in a new architecture we call the co-RCC flexure pivot oscillator. In this realization, the isochronism defect of the oscillator is controlled by adjusting the stiffness of parallel flexures before fabrication through their length Lp, which has no effect on any other crucial property, including nominal frequency. We show that this method is also compatible with post-fabrication tuning by laser ablation. The advantage of our design is that isochronism tuning is an intrinsic part of the oscillator, whereas previous isochronism correctors were mechanisms added to the oscillator. The results of our previous research are also implemented in this mechanism to achieve gravity insensitivity, which is an essential property for mechanical watch time bases. We derive analytical models for the isochronism and gravity sensitivity of the oscillator and validate them by finite element simulation. We give an example of dimensioning this oscillator to reach typical practical watch specifications and show that we can tune the isochronism defect with a resolution of 1 s/day within an operating range of 10% of amplitude. We present a mock-up of the oscillator serving as a preliminary proof-of-concept.

scholarly journals Conceptual design of a rotational mechanical time base with varying inertia

2019 ◽  
Author(s):  
Etienne Thalmann ◽  
Simon Henein
Keyword(s):  
Elastic Properties ◽  
Conceptual Design ◽  
Rotational Symmetry ◽  
Elastic Behavior ◽  
Time Base ◽  
Coupled Oscillator ◽  
New Family ◽  
Spiral Spring ◽  
Nonlinear Elastic

Flexure pivot oscillators have the potential to advantageously replace the traditional balance wheel-spiral spring oscillator used in mechanical watches due to their significantly lower friction. However, they have inherent nonlinear elastic properties that can introduce a variation of their frequency with amplitude called isochronism defect. Previous research has focused on controlling the elastic behavior of flexure pivot oscillators to reach isochronism. We present a new way of minimizing the isochronism defect of rotational oscillators by varying their inertia. This principle is embodied in a new family of oscillators we call rotation-dilation coupled oscillator (RDCO). Their architecture also presents a rotational symmetry that is advantageous for minimizing the effects of gravity on their period. We present a description of this new oscillator family, give conceptual tools for tuning its isochronism and show examples of physical implementations.

Design of Microfabricated Mechanically Interlocking Metamaterials for Reworkable Heterogeneous Integration

2021 ◽  
Author(s):  
Geoffrey Garcia ◽  
Kody Wakumoto ◽  
Joseph Brown
Keyword(s):  
Analytical Models ◽  
Elastic Behavior ◽  
Heterogeneous Integration ◽  
Element Analysis ◽  
Microelectronic Devices ◽  
Mechanical Metamaterials ◽  
Dry Adhesives ◽  
Cantilever Array ◽  
Mechanical Bonding ◽  
Interconnect Technology

Abstract Next–generation interconnects utilizing mechanically interlocking structures enable permanent and reworkable joints between microelectronic devices. Mechanical metamaterials, specifically dry adhesives, are an active area of research which allows for the joining of objects without traditional fasteners or adhesives, and in the case of chip integration, without solder. This paper focuses on reworkable joints that enable chips to be removed from their substrates to support reusable device prototyping and packaging, creating the possibility for eventual pick-and-place mechanical bonding of chips with no additional bonding steps required. Analytical models are presented and are verified through Finite Element Analysis (FEA) assuming pure elastic behavior. Sliding contact conditions in FEA simplify consideration of several design variations but contribute ~10% uncertainty relative to experiment, analysis, and point-loaded FEA. Two designs are presented; arrays of flat cantilevers have a bond strength of 6.3 kPa, and non-flat cantilevers have a strength of 29 kPa. Interlocking designs present self-aligning in-plane forces that emerge from translational perturbation from perfect alignment. Stresses exceeding the material yield stress during adhesion operations present a greater concern for repeatable operation of compliant interlocking joints and will require further study quantifying and accommodating plastic deformation. Designs joining a rigid array with a complementary compliant cantilever array preserve the condition of reworkability for the surface presenting the rigid array. Eventual realization of interconnect technology based on this study will provide a great improvement of functionality and adaptability in heterogeneous integration and microdevice packaging.

scholarly journals A set of measures for the systematic classification of the nonlinear elastic behavior of disparate rocks

2015 ◽  
Vol 120 (3) ◽  
pp. 1587-1604 ◽  
Author(s):  
Jacques Rivière ◽  
Parisa Shokouhi ◽  
Robert A. Guyer ◽  
Paul A. Johnson
Keyword(s):  
Elastic Behavior ◽  
Systematic Classification ◽  
Nonlinear Elastic

Multiscale Issues in DNS of Multiphase Flows

2011 ◽  
Author(s):  
Bahman Aboulhasanzadeh ◽  
Siju Thomas ◽  
Jiacai Lu ◽  
Gretar Tryggvason
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Multiphase Flows ◽  
Analytical Models ◽  
Small Scale ◽  
Layer Model ◽  
Inertia Effects ◽  
Thin Film Model ◽  
Simple Boundary ◽  
Separation Of Scales

In direct numerical simulations (DNS) of multiphase flows it is frequently found that features much smaller than the “dominant” flow scales emerge. Those features consist of thin films, filaments, drops, and boundary layers, and usually surface tension is strong so the geometry is simple. Inertia effects are also small so the flow is simple and often there is a clear separation of scales between those features and the rest of the flow. Thus it is often possible to describe the evolution of this flow by analytical models. Here we discuss two examples of the use of analytical models to account for small-scale features in DNS of multiphase flows. For the flow in the film beneath a drop sliding down a sloping wall we capture the evolution of films that are too thin to be accurately resolved using a grid that is sufficient for the rest of the flow by a thin film model. The other example is the mass transfer from a gas bubbly rising in a liquid. Since diffusion of mass is much slower than the diffusion of momentum, the mass transfer boundary layer is very thin and can be captured by a simple boundary layer model.

Digital image correlation to analyze nonlinear elastic behavior of materials

2017 ◽  
Author(s):  
Nirusha Phillips ◽  
Ghulam Mubashar Hassan ◽  
Arcady Dyskin ◽  
Cara MacNish ◽  
Elena Pasternak
Keyword(s):  
Digital Image Correlation ◽  
Digital Image ◽  
Image Correlation ◽  
Elastic Behavior ◽  
Nonlinear Elastic

scholarly journals Random Fiber Networks With Superior Properties Through Network Topology Control

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
S. Deogekar ◽  
Z. Yan ◽  
R. C. Picu
Keyword(s):  
Network Architecture ◽  
Elastic Behavior ◽  
Fiber Networks ◽  
Linear Elastic ◽  
New Class ◽  
Link Density ◽  
Cross Link Density ◽  
Random Fiber Networks ◽  
Nonlinear Elastic ◽  
Poisson Contraction

In this work, we study the effect of network architecture on the nonlinear elastic behavior and strength of athermal random fiber networks of cellular type. We introduce a topology modification of Poisson–Voronoi (PV) networks with convex cells, leading to networks with stochastic nonconvex cells. Geometric measures are developed to characterize this new class of nonconvex Voronoi (NCV) networks. These are softer than the reference PV networks at the same nominal network parameters such as density, cross-link density, fiber diameter, and connectivity number. Their response is linear elastic over a broad range of strains, unlike PV networks that exhibit a gradual increase of the tangent stiffness starting from small strains. NCV networks exhibit much smaller Poisson contraction than any network of same nominal parameters. Interestingly, the strength of NCV networks increases continuously with an increasing degree of nonconvexity of the cells. These exceptional properties render this class of networks of interest in a variety of applications, such as tissue scaffolds, nonwovens, and protective clothing.

A Pump-Probe Analysis of Nonlinear Elastic Behavior on the San Andreas Fault

2020 ◽  
Author(s):  
Andrew Delorey
Keyword(s):  
San Andreas Fault ◽  
Earth Tides ◽  
Elastic Behavior ◽  
Fracture Networks ◽  
Pump Probe ◽  
San Andreas ◽  
The Earth ◽  
Probe Analysis ◽  
Highly Nonlinear ◽  
Nonlinear Elastic

<p>Fracture networks in the subsurface influence nearly every aspect of earthquakes and natural hazards.  These aspects, including stress, permeability and material failure, and are important for hazard assessment. However, our ability to monitor fracture behavior in the Earth is insufficient for any type of decision-making regarding hazard avoidance.  I propose a new method for probing the evolution of fracture networks in situ to inform public safety decisions and understand natural systems. </p><p>In heterogeneous, fractured materials, like those found in the Earth, the relationship between stress and strain is highly nonlinear.  This nonlinearity in the upper crust is almost entirely due to fractures.  By measuring to what extent Earth materials exhibit nonlinear elastic behavior, we can learn more information about them.  Directly, measuring physical properties may be more useful than just detecting that fractures are present or how they are shaped and oriented.  We measure nonlinearity by measuring the apparent modulus at different strains. </p><p>In this study we use a pump-probe analysis, which involves continuously probing velocity (as a proxy for modulus) while systematically straining the material.  We will use solid Earth tides as a strain pump and empirical Green’s functions (EGF) as a velocity probe.  We apply this analysis to the San Andreas Fault near Parkfield, California.  We chose Parkfield because there is a long-term deployment of borehole seismic instruments that recorded before and after a M6 earthquake.  We find evidence that nonlinear behavior is correlated with the seismic cycle and therefore it may contain information on the both the evolution and current state of stress on faults. </p>

A Robot Gripper in Polymeric Material for Solid Micro-Meso Parts

2017 ◽  
Vol 11 (2) ◽  
pp. 311-321 ◽  
Author(s):  
Francesco Aggogeri ◽  
◽  
Andrea Avanzini ◽  
Alberto Borboni ◽  
Stefano Pandini
Keyword(s):  
Polymeric Material ◽  
Low Cost ◽  
Material Model ◽  
Elastic Behavior ◽  
Mechanical Transmission ◽  
Element Analysis ◽  
Robot Gripper ◽  
Simple Geometry ◽  
Deformable Materials ◽  
Nonlinear Elastic

This paper proposes a robot gripper in polymeric material for solid micro-meso parts. The gripper is developed using a light-weight, highly deformable and low cost material, that allows elastic deformations. The proposed solution consists of a simple geometry, incorporating the complexity of the mechanical transmission in the non-linear high deformations of the flexible elements of the device. This choice permits to grip multi-sizes objects. The design approach focuses on Ludwick material model, that describes deformable materials with a nonlinear elastic behavior. The kinematics of the gripper is presented and the results are verified with the finite element analysis. Finally, the gripper was fabricated and validated through a set of experimetal tests. The obtained resulsts confirmed the theoretical and simultion models. The maximum opening and force of the gripping jaws are 1,500 μm and 155 mN, repsectively. Nevetheless further performances may be obtained using different geometrical choices developed in the kinematic analysis.

scholarly journals Nonlinear elastic behavior of bitumen emulsion-stabilized materials with C&D waste aggregates

2015 ◽  
Vol 98 ◽  
pp. 853-863 ◽  
Author(s):  
B. Gómez-Meijide ◽  
I. Pérez
Keyword(s):  
Elastic Behavior ◽  
Bitumen Emulsion ◽  
Nonlinear Elastic
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