A Geometric Theory for Form, Profile and Orientation Tolerances: Evaluation Algorithms and Simulation Results

1998 ◽  
Author(s):  
J. B. Gou ◽  
Y. X. Chu ◽  
Z. X. Li
Keyword(s):  
Minimization Problem ◽  
Software Package ◽  
Initial Conditions ◽  
Geometric Theory ◽  
Simulation Experiments ◽  
Extensive Simulation ◽  
Minimum Zone ◽  
Linear Programming Problems ◽  
Simulation Results ◽  
Tolerance Verification

Abstract Using the geometric theory for formulation of form, profile and orientation tolerances, we develop a simple geometric algorithm, called the Symmetric Minimum Zone (SMZ) algorithm, to unify the computation of form, profile and orientation tolerances. First, using a technique of numerical analysis, we transform the non-differentiable minimization problem into a differentiable minimization problem over an extended configuration space. Then, we solve the latter problem by computing the solutions of a sequence of linear programming problems which can be easily derived using the geometric properties of SE(3)/G0. The SMZ algorithm is incorporated into a software package called GTPack for tolerance verification. Numerous simulation experiments show that the SMZ algorithm has several important features which could lead to its rapid acceptance in the industry: (1) consistency with the Y14.5M standard, (2) computational efficiency, (3) robustness with respect to variations in initial conditions; and (4) implementational simplicity. We also give extensive simulation results comparing the performances of the SMZ algorithm against the best known algorithms in the literature.

A Geometric Theory for Formulation of Form, Profile and Orientation Tolerances: Problem Formulation

1998 ◽  
Author(s):  
J. B. Gou ◽  
Y. X. Chu ◽  
H. Wu ◽  
Z. X. Li
Keyword(s):  
Configuration Space ◽  
Minimization Problem ◽  
Geometric Theory ◽  
Problem Formulation ◽  
Euclidean Group ◽  
Geometric Properties ◽  
Symmetry Subgroup ◽  
Minimum Zone ◽  
Constrained Minimization Problem ◽  
Linear Programming Problems

Abstract This paper develops a geometric theory which unifies the formulation and evaluation of form (straightness, flatness, cylindricity and circularity), profile and orientation tolerances stipulated in ANSI Y14.5M standard. In the paper, based on an an important observation that a toleranced feature exhibits a symmetry subgroup G0 under the action of the Euclidean group, SE(3), we identify the configuration space of a toleranced (or a symmetric) feature with the homogeneous space SE(3)/G0 of the Euclidean group. Geometric properties of SE(3)/G0, especially its exponential coordinates carried over from that of SE(3), are analyzed. We show that all cases of form, profile and orientation tolerances can be formulated as a minimization or constrained minimization problem on the space SE(3)/G0, with G0 being the symmetry subgroup of the underlying feature. We transform the non-differentiable minimization problem into a differentiable minimization problem over an extended configuration space. Using geometric properties of SE(3)/G0, we derive a sequence of linear programming problems whose solutions can be used to approximate the minimum zone solutions.

A simulated global GM estimate of the asteroid 469219 Kamo‘oalewa for China’s future asteroid mission

2020 ◽  
Vol 493 (3) ◽  
pp. 4012-4021 ◽  
Author(s):  
W T Jin ◽  
F Li ◽  
J G Yan ◽  
T P Andert ◽  
M Ye ◽  
...  
Keyword(s):  
Software Package ◽  
Initial Conditions ◽  
Weighted Least Squares ◽  
Reliable Estimate ◽  
Distance Measurements ◽  
Radio Science ◽  
Least Squares Fit ◽  
Asteroid Mission ◽  
Sample Return Mission ◽  
Simulation Results

ABSTRACT China will launch in the forthcoming years a sample return mission called ZhengHe, to asteroid 469219 Kamo‘oalewa (provisional designation 2016HO3) and comet 133P/Elst-Pizarro. The mission will consist of an orbiter and a nano-lander. One of ZhengHe’s investigations is the radio science experiment, whose main objective is the asteroid GM estimate. In this paper, we conduct full numerical simulations of the radio science experiment using the wudogs software package, developed by Wuhan University. In addition to two-way Doppler measurements, we also include one-way on-board distance measurements. A list of parameters including the spacecraft initial conditions and the global asteroid GM are solved using a weighted least-squares fit. The simulation results indicate that the GM solution is very sensitive to the ephemeris error. We need an accuracy within 2 km on the ephemeris of the asteroid to achieve a reliable estimate of GM.

Corner-Boundary Processor Allocation for 3D Mesh-Connected Multicomputers

2015 ◽  
Vol 5 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Ismail M. Ababneh ◽  
Saad Bani-Mohammad ◽  
Motasem Al Smadi
Keyword(s):  
System Performance ◽  
Allocation Strategy ◽  
Processor Allocation ◽  
Simulation Experiments ◽  
3D Mesh ◽  
Extensive Simulation ◽  
System Utilization ◽  
Free List ◽  
Simulation Results ◽  
Allocation Strategies

This research paper presents a new contiguous allocation strategy for 3D mesh-connected multicomputers. The proposed strategy maintains a list of maximal free sub-meshes and gives priority to allocating corner and boundary free sub-meshes. The goal of corner and boundary allocation is to decrease the number of leftover free sub-meshes and increase their sizes, which is expected to reduce processor fragmentation and improve overall system performance. The proposed strategy, which is referred to as Turning Corner-Boundary Free List (TCBFL) strategy, is compared, using extensive simulation experiments, to several existing allocation strategies for 3D meshes. These are the First-Fit (FF), Turning First-Fit Free List (TFFFL), and Turning Busy List (TBL) allocation strategies. The simulation results show that TCBFL produces average turnaround times and mean system utilization values that are superior to those of previous strategies.

On the Hybrid Workpiece Localization/Inspection/Machinability Problem

1999 ◽  
Author(s):  
Y. X. Chu ◽  
K. Cao ◽  
H. Wu ◽  
Z. X. Li
Keyword(s):  
Linear Programming ◽  
Optimization Problems ◽  
Geometric Theory ◽  
Cad Model ◽  
Constrained Optimization Problems ◽  
Minimum Zone ◽  
On Line ◽  
Workpiece Localization ◽  
Simulation Results ◽  
Present Simulation

Abstract This work addresses the localization, inspection and machinability problem of a workpiece. It includes the problem of aligning the CAD model of a workpiece such that all points measured on the finished surfaces of the workpiece match closely to corresponding surfaces on the model with minimum zone tolerances while all unmachined surfaces lie outside the model and have the maximal machinable volume. This is referred to as the hybrid localization/inspection/machinability problem and has important applications in setting up and inspecting of partially finished workpieces. This paper first gives a formulation of the hybrid problem using differential geometric theory and the minimax method, then proposes a methodology for treating localization, on-line inspection and machinability of workpieces simultaneously. The hybrid problem is decoupled into a (symmetric) localization/inspection problem and a machinability problem using the geometric properties of the hybrid problem. Then both problems are formulated as constrained optimization problems and transformed into linear programming (LP) problems to solve them easily. Finally we present simulation results to demonstrate efficiency of our method for the hybrid problem.

Dynamics of the macromolecular composition of the biomass of microalgae in the morning under natural light. Model

2020 ◽  
pp. 45-52
Author(s):  
Alexander S. Lelekov ◽  
Anton V. Shiryaev
Keyword(s):  
Biochemical Composition ◽  
Initial Conditions ◽  
Natural Light ◽  
Photoautotrophic Growth ◽  
Structural Part ◽  
Basic Model ◽  
Microalgae Culture ◽  
Simulation Results ◽  
Structural Parts ◽  
Macromolecular Composition

The work is devoted to modeling the growth of optically dense microalgae cultures in natural light. The basic model is based on the idea of the two-stage photoautotrophic growth of microalgae. It is shown that the increase in the intensity of sunlight in the first half of the day can be described by a linear equation. Analytical equations for the growth of biomass of microalgae and its macromolecular components are obtained. As the initial conditions, it is assumed that at the time of sunrise, the concentration of reserve biomass compounds is zero. The simulation results show that after sunrise, the growth of the microalgae culture is due only to an increase in the reserve part of the biomass, while the structural part practically does not change over six hours. Changes in the ratio of the reserve and structural parts of the biomass indicate a change in the biochemical composition of cells.

scholarly journals Simulations of Switchback, Fragmentation and Sunspot Pair in δ-Sunspots during Magnetic Flux Emergence

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 586
Author(s):  
Che-Jui Chang ◽  
Jean-Fu Kiang
Keyword(s):  
Magnetic Field ◽  
Solar System ◽  
Field Strength ◽  
Magnetic Flux ◽  
Initial Conditions ◽  
Observation Data ◽  
Flux Emergence ◽  
Polarity Inversion ◽  
Simulation Results ◽  
Spot Type

Strong flares and coronal mass ejections (CMEs), launched from δ-sunspots, are the most catastrophic energy-releasing events in the solar system. The formations of δ-sunspots and relevant polarity inversion lines (PILs) are crucial for the understanding of flare eruptions and CMEs. In this work, the kink-stable, spot-spot-type δ-sunspots induced by flux emergence are simulated, under different subphotospheric initial conditions of magnetic field strength, radius, twist, and depth. The time evolution of various plasma variables of the δ-sunspots are simulated and compared with the observation data, including magnetic bipolar structures, relevant PILs, and temperature. The simulation results show that magnetic polarities display switchbacks at a certain stage and then split into numerous fragments. The simulated fragmentation phenomenon in some δ-sunspots may provide leads for future observations in the field.

scholarly journals Limits of reproducibility and hydrodynamic noise in atmospheric regional modelling

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Beate Geyer ◽  
Thomas Ludwig ◽  
Hans von Storch
Keyword(s):  
Regional Climate Model ◽  
Computer Architecture ◽  
Climate Model ◽  
Initial Conditions ◽  
Regional Climate ◽  
Quality Criterion ◽  
Dynamic State ◽  
Regional Modelling ◽  
Simulation Results ◽  
Mathematical Operations

AbstractReproducibility of research results is a fundamental quality criterion in science; thus, computer architecture effects on simulation results must be determined. Here, we investigate whether an ensemble of runs of a regional climate model with the same code on different computer platforms generates the same sequences of similar and dissimilar weather streams when noise is seeded using different initial states of the atmosphere. Both ensembles were produced using a regional climate model named COSMO-CLM5.0 model with ERA-Interim forcing. Divergent phase timing was dependent on the dynamic state of the atmosphere and was not affected by noise seeded by changing computers or initial model state variations. Bitwise reproducibility of numerical results is possible with such models only if everything is fixed (i.e., computer, compiler, chosen options, boundary values, and initial conditions) and the order of mathematical operations is unchanged between program runs; otherwise, at best, statistically identical simulation results can be expected.

scholarly journals Extended and Unscented Kalman Filtering Applied to a Flexible-Joint Robot with Jerk Estimation

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Mohammad Ali Badamchizadeh ◽  
Iraj Hassanzadeh ◽  
Mehdi Abedinpour Fallah
Keyword(s):  
Initial Conditions ◽  
Covariance Matrices ◽  
Flexible Joints ◽  
Velocity Measurements ◽  
Lagrange Equations ◽  
Robust Nonlinear Control ◽  
Flexible Joint ◽  
Flexible Joint Robots ◽  
Simulation Results

Robust nonlinear control of flexible-joint robots requires that the link position, velocity, acceleration, and jerk be available. In this paper, we derive the dynamic model of a nonlinear flexible-joint robot based on the governing Euler-Lagrange equations and propose extended and unscented Kalman filters to estimate the link acceleration and jerk from position and velocity measurements. Both observers are designed for the same model and run with the same covariance matrices under the same initial conditions. A five-bar linkage robot with revolute flexible joints is considered as a case study. Simulation results verify the effectiveness of the proposed filters.

Investigating the NO-dependent photooxidation of limonene by OH and O3 using the atmosphere simulation chamber SAPHIR

2021 ◽  
Author(s):  
Yat Sing Pang ◽  
Martin Kaminski ◽  
Anna Novelli ◽  
Philip Carlsson ◽  
Ismail-Hakki Acir ◽  
...  
Keyword(s):  
Organic Aerosol ◽  
Oxidation Products ◽  
Chemical Mechanism ◽  
Reaction Pathways ◽  
Oh Radicals ◽  
Oh Radical ◽  
Simulation Experiments ◽  
Master Chemical Mechanism ◽  
Simulation Results ◽  
Atmosphere Simulation Chamber

<p>Limonene is the fourth-most abundant monoterpene in the atmosphere, which upon oxidation leads to the formation of secondary organic aerosol (SOA) and thereby influences climate and air quality.</p><p>In this study, the oxidation of limonene by OH at different atmospherically relevant NO and HO<sub>2</sub> levels (NO: 0.1 – 10 ppb; HO<sub>2</sub>: 20 ppt) was investigated in simulation experiments in the SAPHIR chamber at Forschungszentrum Jülich. The analysis focuses on comparing measured radical concentrations (RO<sub>2</sub>, HO<sub>2</sub>, OH) and OH reactivity (k<sub>OH</sub>) with modeled values calculated using the Master Chemical Mechanism (MCM) version 3.3.1.</p><p>At high and medium NO concentrations, RO<sub>2</sub> is expected to quickly react with NO. An HO<sub>2</sub> radical is produced during the process that can be converted back to an OH radical by another reaction with NO. Consistently, for experiments conducted at medium NO levels (~0.5 ppb, RO<sub>2</sub> lifetime ~10 s), simulated RO<sub>2</sub>, HO<sub>2</sub>, and OH agree with observations within the measurement uncertainties, if the OH reactivity of oxidation products is correctly described.</p><p>At lower NO concentrations, the regeneration of HO<sub>2</sub> in the RO<sub>2</sub> + NO reaction is slow and the reaction of RO<sub>2</sub> with HO<sub>2</sub> gains importance in forming peroxides. However, simulation results show a large discrepancy between calculated radical concentrations and measurements at low NO levels (<0.1 ppb, RO<sub>2</sub> lifetime ~ 100 s). Simulated RO<sub>2</sub> concentrations are found to be overestimated by a factor of three; simulated HO<sub>2</sub> concentrations are underestimated by 50 %; simulated OH concentrations are underestimated by about 35%, even if k<sub>OH</sub> is correctly described. This suggests that there could be additional RO<sub>2</sub> reaction pathways that regenerate HO<sub>2</sub> and OH radicals become important, but they are not taken into account in the MCM model.</p>

scholarly journals Numerical Analysis of the Transport and Fate of Nitrate in the Soil and Nitrate Leaching to Drains

2001 ◽  
Vol 1 ◽  
pp. 170-180 ◽  
Author(s):  
Alaa El-Sadek ◽  
Mona Radwan ◽  
Jan Feyen
Keyword(s):  
Nitrate Leaching ◽  
Initial Conditions ◽  
Continuous Cropping ◽  
Nitrogen Transport ◽  
State Variables ◽  
Nitrogen Application ◽  
Transport And Transformation ◽  
Bottom Boundary Condition ◽  
Rainfall Depth ◽  
Simulation Results

In this study, the transport and fate of nitrate within the soil profile and nitrate leaching to drains were analyzed by comparing historic field data with the simulation results of the DRAINMOD model. The nitrogen version of DRAINMOD was used to simulate the performance of the nitrogen transport and transformation of the Hooibeekhoeve experiment, situated in the sandy region of the Kempen (Belgium) and conducted for a 30-year (1969–1998) period. In the analysis, a continuous cropping with maize was assumed. Comparisons between experimentally measured and simulated state variables indicate that the nitrate concentrations in the soil and nitrate leaching to drains are controlled by the fertilizer practice, the initial conditions, and the rainfall depth and distribution. Furthermore, the study reveals that the model used gives a fair description of the nitrogen dynamics in the soil and subsurface drainage at field scale. From the comparative analysis between experimental data and simulation results it can also be concluded that the model after calibration is a useful tool to optimize as a function of the combination “climate-crop-soil-bottom boundary condition” the nitrogen application strategy resulting in an acceptable level of nitrate leaching for the environment.

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