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Selected Works

2013

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Articles 1 - 30 of 47

Full-Text Articles in Mechanical Engineering

A Five-Level Three-Phase Hybrid Cascade Multilevel Inverter Using A Single Dc Source For A Pm Synchronous Motor Drive, John N. Chiasson, Burak Ozpineci, Leon M. Tolbert Dec 2013

A Five-Level Three-Phase Hybrid Cascade Multilevel Inverter Using A Single Dc Source For A Pm Synchronous Motor Drive, John N. Chiasson, Burak Ozpineci, Leon M. Tolbert

Burak Ozpineci

The interest here is in using a single DC power source to construct a 3-phase 5-level cascade multilevel inverter to be used as a drive for a PM traction motor. The 5-level inverter consists of a standard 3-leg inverter (one leg for each phase) and an H-bridge in series with each inverter leg, which use a capacitor as a DC source. It is shown that one can simultaneously maintain the regulation of the capacitor voltage while achieving an output voltage waveform which is 25% higher than that obtained using a standard 3-leg inverter by itself.


Loading Path Determination For Tube Hydroforming Process Of Automotive Component Using Apdl, E. Masoumi Khalil Abad, Amir Ghazanfari, R. Hashemi Nov 2013

Loading Path Determination For Tube Hydroforming Process Of Automotive Component Using Apdl, E. Masoumi Khalil Abad, Amir Ghazanfari, R. Hashemi

Amir Armani (Ghazanfari)

In this study, an extended stress-based forming limit diagram (FLD) for prediction of necking based on the Marciniak and Kucznski (M-K) model is represented and applied in tube hydroforming. The bulge forming of a straight tube is simulated by finite element method and verified with published experimental data. This adaptive simulation technique is based on the ability to detect the onset and growth of defects (e.g., bursting and wrinkling) and to promptly readjust the loading paths. Thus, a suitable load path is determined by applying Adaptive Simulation Method in ANSYS Parametric Design Language (APDL).


A Proposed Learner-Centered Mechatronics Engineering Instructional Program, Patrick N. Currier, Richard Goff, Janis Terpenny Nov 2013

A Proposed Learner-Centered Mechatronics Engineering Instructional Program, Patrick N. Currier, Richard Goff, Janis Terpenny

Patrick N. Currier

This paper examines the need and requirements for a mechatronics degree program. The results of a survey of the few existing programs in this field are provided. Then, using a case study example for Virginia Tech, a proposed mechatronics curriculum based on a learner-centered paradigm is described. The curriculum combines existing courses in mechanical, electrical, and computer engineering with new, hands-on courses to provide students with a chance to practice and explore the subject matter in ways consistent with the demands of both industry and accreditation. This program, if implemented, could provide a university with a unique offering to attract …


A Novel Method For Prediction Of Mobile Robot Maneuvering Spaces, Patrick N. Currier, Alfred L. Wicks Oct 2013

A Novel Method For Prediction Of Mobile Robot Maneuvering Spaces, Patrick N. Currier, Alfred L. Wicks

Patrick N. Currier

As the operational uses of mobile robots continue to expand, it becomes useful to be able to predict the admissible maneuvering space to prevent the robot from executing unsafe maneuvers. A novel method is proposed to address this need by using force-moment diagrams to characterize the robot’s maneuvering space in terms of path curvature and curvature rate. Using the proposed superposition techniques, these diagrams can then be transformed in real-time to provide a representation of the permissible maneuvering space while allowing for changes in the robot’s loading and terrain conditions. Simulation results indicate that the technique can be applied to …


An Experimental And Modeling Study Of Formaldehyde And 1,3,5-Trioxane Flame Chemistry, Jeffrey S. Santner, Francis M. Haas, Frederick L. Dryer, Yiguang Ju Sep 2013

An Experimental And Modeling Study Of Formaldehyde And 1,3,5-Trioxane Flame Chemistry, Jeffrey S. Santner, Francis M. Haas, Frederick L. Dryer, Yiguang Ju

Francis (Mac) Haas

Formaldehyde is a key species produced during oxidation of virtually all hydrocarbon and oxygenated fuels, and it is also a regulated hazardous air pollutant. An improved understanding of its formation and destruction chemistry is therefore vital to the study of many energy conversion processes. To this end, this work experimentally and numerically investigates the flame chemistry of formaldehyde (CH2O) at atmospheric pressure. The laminar burning rate of 1,3,5-trioxane/O2/N2 mixtures is measured in outwardly propagating spherical flames, where high concentrations of formaldehyde are generated early in the flame structure from decomposition of 1,3,5-trioxane.
Though laminar burning rate predictions of several combustion …


Evaluation Of Thermal Radiation Effects On Apparent Propagation Rates Of High Pressure Spherical Flames, Jeffrey S. Santner, Francis M. Haas, Yiguang Ju, Frederick L. Dryer Sep 2013

Evaluation Of Thermal Radiation Effects On Apparent Propagation Rates Of High Pressure Spherical Flames, Jeffrey S. Santner, Francis M. Haas, Yiguang Ju, Frederick L. Dryer

Francis (Mac) Haas

Thermal radiation is usually not considered in the interpretation of laminar burning rates measured by the outwardly propagating spherical flame method. However, it may contribute significantly to measurement uncertainty, especially for model-constraining conditions at lower flame temperatures and higher pressures. The present work derives a conservative analytical estimate of the effects of radiation heat loss, which include radiation-induced burned gas motion, decreasing flame temperature due to conduction to the radiating burned gas, and radiation loss from the flame zone. Detailed numerical simulations covering a range of burning conditions serve to validate this analytical tool. Modeling results from both detailed simulation …


Evaluating The Performance Of Fault Detection And Diagnostics Protocols Applied To Air-Cooled Unitary Air-Conditioning Equipment, David P. Yuill, James E. Braun Sep 2013

Evaluating The Performance Of Fault Detection And Diagnostics Protocols Applied To Air-Cooled Unitary Air-Conditioning Equipment, David P. Yuill, James E. Braun

David Yuill

Fault detection and diagnostics (FDD) tools are increasingly being applied to air-cooled unitary air-conditioning systems. However, it is not known how well these tools work because there is no standard method of measuring or evaluating the performance of FDD. In the current paper the authors describe the common faults that FDD is applied to in unitary systems, and propose a method of evaluating the performance of FDD protocols. The method involves feeding measurement data through a candidate protocol and collecting and organizing the responses based upon the fault’s impacts on performance. A library of faulted and unfaulted measurement data has …


Toward A Gpu-Accelerated Immersed Boundary Method For Wind Forecasting Over Complex Terrain, Rey Deleon, Kyle Felzien, Inanc Senocak Sep 2013

Toward A Gpu-Accelerated Immersed Boundary Method For Wind Forecasting Over Complex Terrain, Rey Deleon, Kyle Felzien, Inanc Senocak

Inanc Senocak

A short-term wind power forecasting capability can be a valuable tool in the renewable energy industry to address load-balancing issues that arise from intermittent wind fields. Although numerical weather prediction models have been used to forecast winds, their applicability to micro-scale atmospheric boundary layer flows and ability to predict wind speeds at turbine hub height with a desired accuracy is not clear. To address this issue, we develop a multi-GPU parallel flow solver to forecast winds over complex terrain at the micro-scale, where computational domain size can range from meters to several kilometers. In the solver, we adopt the immersed …


Finite Element Analysis Of The Ramberg-Osgood Bar, Dongming Wei Aug 2013

Finite Element Analysis Of The Ramberg-Osgood Bar, Dongming Wei

Dongming Wei

In this work, we present a priori error estimates of finite element approximations of the solution for the equilibrium equation of an axially loaded Ramberg-Osgood bar. The existence and uniqueness of the solution to the associated nonlinear two point boundary value problem is established and used as a foundation for the finite element analysis.


3d Modelling Of Limestone Reactions In Oxygen Fired Cfb, Sirpa Rahiala, Kari Myöhänen, Timo Hyppänen Aug 2013

3d Modelling Of Limestone Reactions In Oxygen Fired Cfb, Sirpa Rahiala, Kari Myöhänen, Timo Hyppänen

Kari Myöhänen

No abstract provided.


Non-Destructive Testing (Ndt) By Laser Shearography And Fringe Projection, Xiaoran Chen, Morteza Khaleghi, Ivo Dobrev, Cosme Furlong Jul 2013

Non-Destructive Testing (Ndt) By Laser Shearography And Fringe Projection, Xiaoran Chen, Morteza Khaleghi, Ivo Dobrev, Cosme Furlong

Morteza Khaleghi

Non-destructive testing (NDT) is critical to many precision industries because it can provide important information about the structural health of critical components and systems. In addition, NDT can also identify situations that could potentially lead to critical failures. Specifically, NDT by optical methods have become popular because of their non-contact and non-invasive nature. Shearography is a high-resolution optical NDT method for identification and characterization of structural defects in components and has gained wide acceptance over the last decade; however, as a drawback, shearography cannot locate the position of defects in 3D. To overcome this limitation, we are combining shearography with …


Development Of A Novel Handheld Device For Active Compensation Of Physiological Tremor, Abhijit Saxena Jul 2013

Development Of A Novel Handheld Device For Active Compensation Of Physiological Tremor, Abhijit Saxena

Abhijit Saxena

In microsurgery, the human hand imposes certain limitations in accurately positioning the tip of a device such as scalpel. Any errors in the motion of the hand make microsurgical procedures difficult and involuntary motions such as hand tremors can make some procedures significantly difficult to perform. This is particularly true in the case of vitreoretinal microsurgery. The most familiar source of involuntary motion is physiological tremor. Real-time compensation of tremor is, therefore, necessary to assist surgeons to precisely position and manipulate the tool-tip to accurately perform a microsurgery. In this thesis, a novel handheld device (AID) is described for compensation …


Optimization Of Multilayer Wear-Resistant Thin Films Using Finite Element Analysis On Stiff And Compliant Substrates, R. K. Lakkaraju, Florin Bobaru, S. L. Rohde Jul 2013

Optimization Of Multilayer Wear-Resistant Thin Films Using Finite Element Analysis On Stiff And Compliant Substrates, R. K. Lakkaraju, Florin Bobaru, S. L. Rohde

Florin Bobaru Ph.D.

Extensive research has been carried out by researchers on the growth and characterization of multilayer protective coatings, but the design of these coatings still remains largely empirical. In this regard, recent progress has been made in developing a design approach for optimizing a multilayer coating structure before deposition, which would help save time and material. In pursuit of an optimal design, finite element analysis using a plane strain Hertzian contact model was developed to investigate the stress/ strain behavior within the layers of the system. The present study looks to find the optimal thicknesses of individual layers in a multilayer …


The Formulation And Computation Of The Nonlocal J-Integral In Bond-Based Peridynamics, Wenke Hu, Youn Doh Ha, Florin Bobaru, Stewart A. Silling Jul 2013

The Formulation And Computation Of The Nonlocal J-Integral In Bond-Based Peridynamics, Wenke Hu, Youn Doh Ha, Florin Bobaru, Stewart A. Silling

Florin Bobaru Ph.D.

This work presents a rigorous derivation for the formulation of the J-integral in bond-based peridynamics using the crack infinitesimal virtual extension approach. We give a detailed description of an algorithm for computing this nonlocal version of the J-integral.We present convergence studies (m-convergence and δ-convergence) for two different geometries: a single edge-notch configuration and a double edge-notch sample.We compare the results with results based on the classical J-integral and obtained from FEM calculations that employ special elements near the crack tip.We identify the size of the nonlocal region for which the peridynamic J-integral value is near the classical FEM solutions.We discuss …


The Meaning, Selection, And Use Of The Peridynamic Horizon And Its Relation To Crack Branching In Brittle Materials, Florin Bobaru, Wenke Hu Jul 2013

The Meaning, Selection, And Use Of The Peridynamic Horizon And Its Relation To Crack Branching In Brittle Materials, Florin Bobaru, Wenke Hu

Florin Bobaru Ph.D.

This note discusses the peridynamic horizon (the nonlocal region around a material point), its role, and practical use in modeling. The objective is to eliminate some misunderstandings and misconceptions regarding the peridynamic horizon. An example of crack branching in a nominally brittle material (homalite) is addressed and we show that crack branching takes place without wave interaction. We explain under what conditions the crack propagation speed depends on the horizon size and the role of incident stress waves on this speed.


Force Chains And Resonant Behavior In Bending Of A Granular Layer On An Elastic Support, Kitti Rattanadit, Florin Bobaru, Konlayut Promratana, Joseph A. Turner Jul 2013

Force Chains And Resonant Behavior In Bending Of A Granular Layer On An Elastic Support, Kitti Rattanadit, Florin Bobaru, Konlayut Promratana, Joseph A. Turner

Florin Bobaru Ph.D.

In this paper we investigate the interaction between a granular layer and an elastic foundation using a coupled Discrete Element Method-Finite Element Method (DEM–FEM) computational model. We use this dynamics code to simulate quasi-static bending of the granular layer and we observe the changes taking place in the structure of the force chains for two cases: with and without rolling resistance. A reversal of the arches formed in the force chains leads to a bending resistance similar to that observed in dynamic experiments on resonant behavior under bending of a layer of sand in a container with an elastic bottom. …


Editorial: Advances In The Dynamics Of Granular Materials, Florin Bobaru, J. S. Chen, Joseph A. Turner Jul 2013

Editorial: Advances In The Dynamics Of Granular Materials, Florin Bobaru, J. S. Chen, Joseph A. Turner

Florin Bobaru Ph.D.

Granular materials exhibit a complex array of phenomena which makes the prediction of their behavior extremely difficult. Granular materials are strongly dissipative and show collective (heap formation, jamming) and size segregation phenomena, and can propagate surface waves. They display fluidization and convective motion, and under certain vibration regimes, they tend to mix when they would otherwise segregate, and segregate when they might otherwise mix. The wide range of behaviors that granular materials can display has been one of the main factors for which the development of predictive models has continued to remain an open problem. The papers in this Special …


Impact Mechanics And High-Energy Absorbing Materials: Review, Pizhong Qiao, Mijia Yang, Florin Bobaru Jul 2013

Impact Mechanics And High-Energy Absorbing Materials: Review, Pizhong Qiao, Mijia Yang, Florin Bobaru

Florin Bobaru Ph.D.

In this paper a review of impact mechanics and high-energy absorbing materials is presented. We review different theoretical models (rigid-body dynamics, elastic, shock, and plastic wave propagation, and nonclassical or nonlocal models. and computational methods (finite-element, finite-difference, and mesh-free methods. used in impact mechanics. Some recent developments in numerical simulation of impact (e.g., peridynamics) and new design concepts proposed as high energy absorbing materials (lattice and truss structures, hybrid sandwich composites, metal foams, magnetorheological fluids, porous shape memory alloys. are discussed. Recent studies on experimental evaluation and constitutive modeling of strain rate-dependent polymer matrix composites are also presented. Impact damage …


Convergence, Adaptive Refinement, And Scaling In 1d Peridynamics, Florin Bobaru Ph.D., Mijia Yabg Ph.D., Leonardo F. Alves M.S., Stewart A. Silling Ph.D., Ebrahim Askari Ph.D., Jifeng Xu Ph.D. Jul 2013

Convergence, Adaptive Refinement, And Scaling In 1d Peridynamics, Florin Bobaru Ph.D., Mijia Yabg Ph.D., Leonardo F. Alves M.S., Stewart A. Silling Ph.D., Ebrahim Askari Ph.D., Jifeng Xu Ph.D.

Florin Bobaru Ph.D.

We introduce here adaptive refinement algorithms for the non-local method peridynamics, which was proposed (in J. Mech. Phys. Solids 2000; 48:175–209) as a reformulation of classical elasticity for discontinuities and long-range forces. We use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected. We discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1D in the limit of the horizon going to zero. Continuous micromoduli lead to optimal rates of …


E(Fg)2: A New Fixed-Grid Shape Optimization Method, Florin Bobaru Ph.D., Srinivas Rachakonda Jul 2013

E(Fg)2: A New Fixed-Grid Shape Optimization Method, Florin Bobaru Ph.D., Srinivas Rachakonda

Florin Bobaru Ph.D.

We propose a shape optimization method over a fixed grid. Nodes at the intersection with the fixed grid lines track the domain’s boundary. These “floating” boundary nodes are the only ones that can move/appear/disappear in the optimization process. The element-free Galerkin (EFG) method, used for the analysis problem, provides a simple way to create these nodes. The fixed grid (FG) defines integration cells for EFG method. We project the physical domain onto the FG and numerical integration is performed over partially cut cells. The integration procedure converges quadratically. The performance of the method is shown with examples from shape optimization …


Influence Of Van Der Waals Forces On Increasing The Strength And Toughness In Dynamic Fracture Of Nanofibre Networks: A Peridynamic Approach, Florin Bobaru Ph.D. Jul 2013

Influence Of Van Der Waals Forces On Increasing The Strength And Toughness In Dynamic Fracture Of Nanofibre Networks: A Peridynamic Approach, Florin Bobaru Ph.D.

Florin Bobaru Ph.D.

The peridynamic method is used here to analyse the effect of van der Waals forces on the mechanical behaviour and strength and toughness properties of three-dimensional nanofibre networks under imposed stretch deformation. The peridynamic formulation allows for a natural inclusion of long-range forces (such as van der Waals forces) by considering all interactions as ‘long-range’. We use van der Waals interactions only between different fibres and do not need to model individual atoms. Fracture is introduced at the microstructural (peridynamic bond) level for the microelastic type bonds, while van der Waals bonds can reform at any time. We conduct statistical …


Studies Of Dynamic Crack Propagation And Crack Branching With Peridynamics, Youn Doh Ha Ph.D., Florin Bobaru Ph.D. Jul 2013

Studies Of Dynamic Crack Propagation And Crack Branching With Peridynamics, Youn Doh Ha Ph.D., Florin Bobaru Ph.D.

Florin Bobaru Ph.D.

In this paper we discuss the peridynamic analysis of dynamic crack branching in brittle materials and show results of convergence studies under uniform grid refinement (m-convergence) and under decreasing the peridynamic horizon (δ-convergence). Comparisons with experimentally obtained values are made for the crack-tip propagation speed with three different peridynamic horizons.We also analyze the influence of the particular shape of themicro-modulus function and of different materials (Duran 50 glass and soda-lime glass) on the crack propagation behavior. We show that the peridynamic solution for this problem captures all the main features, observed experimentally, of dynamic crack propagation and branching, as well …


Self-Biased 215mhz Magnetoelectric Nems Resonator For Ultra-Sensitive Dc Magnetic Field Detection, Tianxiang Nan Jun 2013

Self-Biased 215mhz Magnetoelectric Nems Resonator For Ultra-Sensitive Dc Magnetic Field Detection, Tianxiang Nan

Tianxiang Nan

High sensitivity magnetoelectric sensors with their lectromechanical resonance frequencies , 200 kHz have been recently demonstrated using gnetostrictive/piezoelectric magnetoelectric eterostructures. In this work, we demonstrate a novel agnetoelectric nano-electromechanical systems (NEMS) resonator with an electromechanical resonance frequency of 215 MHz based on an AlN/(FeGaB/Al2O3) 3 10 magnetoelectric heterostructure for detecting DC magnetic fields. This magnetoelectric NEMS resonator showed a high quality factor of 735, and strong magnetoelectric coupling with a large voltage tunable sensitivity. The admittance of the magnetoelectric NEMS resonator was very sensitive to DC magnetic fields at its electromechanical resonance, which led to a new detection mechanism for …


Spherical Particles In A Low Reynolds Number Flow: A V&V Exercise, Nima Fathi, Peter Vorobieff May 2013

Spherical Particles In A Low Reynolds Number Flow: A V&V Exercise, Nima Fathi, Peter Vorobieff

Nima Fathi

The aim of this investigation is validation and verification of solid particle interaction in a low Reynolds number fluid flows We evaluate the accuracy and reliability of discrete phase element method (DPM) for one/two solid particle interaction in a highly viscous flow in both cylindrical and rectangular Couette flow. The computational results (solution) based on ANSYS/FLUENT 14.0 is validated by experimental data. Unsteady DPM CFD simulations are performed to match the experimental setups. Particle trajectories in cylindrical and rectangular domains are studied. In the experiment, spherical particles are suspended in gravity-stratified Newtonian fluid, thus limiting their motion to a single …


Sugarmap: Location-Less Coverage For Micro-Aerial Sensing Swarms, Aveek Purohit, Zheng Sun, Pei Zhang Apr 2013

Sugarmap: Location-Less Coverage For Micro-Aerial Sensing Swarms, Aveek Purohit, Zheng Sun, Pei Zhang

Zheng Sun

No abstract provided.


Stochastic Reconstruction Of Multiple Source Atmospheric Contaminant Dispersion Events, Derek Wade, Inanc Senocak Mar 2013

Stochastic Reconstruction Of Multiple Source Atmospheric Contaminant Dispersion Events, Derek Wade, Inanc Senocak

Inanc Senocak

Reconstruction of intentional or accidental release of contaminants into the atmosphere using concentration measurements from a sensor network constitutes an inverse problem. An added complexity arises when the contaminant is released from multiple sources. Determining the correct number of sources is critical because an incorrect estimation could mislead and delay response efforts. We present a Bayesian inference method coupled with a composite ranking system to reconstruct multiple source contaminant release events. Our approach uses a multi-source data-driven Gaussian plume model as the forward model to predict the concentrations at sensor locations. Bayesian inference with Markov chain Monte Carlo (MCMC) sampling …


Haptography: Capturing And Recreating The Rich Feel Of Real Surfaces, Katherine J. Kuchenbecker, Joseph Romano, William Mcmahan Mar 2013

Haptography: Capturing And Recreating The Rich Feel Of Real Surfaces, Katherine J. Kuchenbecker, Joseph Romano, William Mcmahan

William McMahan

Haptic interfaces, which allow a user to touch virtual and remote environments through a hand-held tool, have opened up exciting new possibilities for applications such as computer-aided design and robot-assisted surgery. Unfortunately, the haptic renderings produced by these systems seldom feel like authentic re-creations of the richly varied surfaces one encounters in the real world. We have thus envisioned the new approach of haptography, or haptic photography, in which an individual quickly records a physical interaction with a real surface and then recreates that experience for a user at a different time and/or place. This paper presents an overview of …


Haptic Displayof Realistic Tool Contact Via Dynamically Compensated Control Of A Dedicated Actuator, William Mcmahan, Katherine J. Kuchenbecker Mar 2013

Haptic Displayof Realistic Tool Contact Via Dynamically Compensated Control Of A Dedicated Actuator, William Mcmahan, Katherine J. Kuchenbecker

William McMahan

High frequency contact accelerations convey important information that the vast majority of haptic interfaces cannot render. Building on prior work, we present an approach to haptic interface design that uses a dedicated linear voice coil actuator and a dynamic system model to allow the user to feel these signals. This approach was tested through use in a bilateral teleoperation experiment where a user explored three textured surfaces under three different acceleration control architectures: none, constant gain, and dynamic compensation. The controllers that use the dedicated actuator vastly outperform traditional position-position control at conveying realistic contact accelerations. Analysis of root mean …


High Frequency Acceleration Feedback Significantly Increases The Realism Of Haptically Rendered Textured Surfaces, William Mcmahan, Joseph M. Romano, Amal M. Abdul Rahuman, Katherine J. Kuchenbecker Mar 2013

High Frequency Acceleration Feedback Significantly Increases The Realism Of Haptically Rendered Textured Surfaces, William Mcmahan, Joseph M. Romano, Amal M. Abdul Rahuman, Katherine J. Kuchenbecker

William McMahan

Almost every physical interaction generates high frequency vibrations, especially if one of the objects is a rigid tool. Previous haptics research has hinted that the inclusion or exclusion of these signals plays a key role in the realism of haptically rendered surface textures, but this connection has not been formally investigated until now. This paper presents a human subject study that compares the performance of a variety of surface rendering algorithms for a master-slave teleoperation system; each controller provides the user with a different combination of position and acceleration feedback, and subjects compared the renderings with direct tool-mediated exploration of …


Why Patent Drawings Get Rejected Part2, Bernadette Marshall Feb 2013

Why Patent Drawings Get Rejected Part2, Bernadette Marshall

Bernadette Marshall

Last time we discussed why drawings might get rejected. The following are real rejection/objection examples compiled from multiple notices. Each includes our suggested solution. Informal utility drawings; these may include hand drawn sketches, pencil drawings, photographs, photocopies of photographs and drawings with hand written text & numerals. -Notice from USPTO; “All sheets must be reasonably free from cracks, creases, and folds. Each sheet must be reasonably free from erasures and must be free from alterations, overwritings, and interlineations”4. -remedy, formalize the drawings. This usually involves tracing the informal drawings using a CAD program ensuring compliance with all USPTO drawing rules. …