scholarly journals Characterization and Correction of the Geometric Errors using a Confocal Microscope for Extended Topography Measurement, Part II: Experimental Study and Uncertainty Evaluation

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1217 ◽  
Author(s):  
Wang ◽  
Gómez ◽  
Yu
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Confocal Microscope ◽  
Geometric Errors ◽  
Data Partition ◽  
The Monte Carlo Method ◽  
Measurement Results ◽  
The Mean ◽  
The Mathematical Model ◽  
Certified Values

This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment determines the correction coefficients of the mathematical model. The dot grid target is measured, and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analyzed. Uncertainties are evaluated using the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centers, K-means clustering, etc., are the same for the two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of the lateral stage of a confocal microscope is meaningful and practicable.

scholarly journals Characterization and Correction of the Geometric Errors in Using Confocal Microscope for Extended Topography Measurement. Part II: Experimental Study and Uncertainty Evaluation

2019 ◽  
Author(s):  
Chen Wang ◽  
Emilio Gomez ◽  
Yingjie Yu
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Confocal Microscope ◽  
Geometric Errors ◽  
Data Partition ◽  
The Monte Carlo Method ◽  
Measurement Results ◽  
The Mean ◽  
The Mathematical Model ◽  
Certified Values

This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment aims at the determinations of the correction coefficients of the mathematical model. The dot grid target is measured and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analysed. Uncertainties are evaluated with implementation of the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centres, K-means clustering, etc., are the same for both two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of lateral stage of confocal microscope is meaningful and practicable.

A study on the key techniques of application of REVO five-axis system in non-orthogonal coordinate measuring machine

2016 ◽  
Vol 231 (4) ◽  
pp. 730-736 ◽  
Author(s):  
Haitao Zhang ◽  
Shugui Liu ◽  
Xinghua Li
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Coordinate Measuring Machine ◽  
Coordinate Measuring Machines ◽  
Measurement Results ◽  
Measuring Machine ◽  
Key Techniques ◽  
Five Axis ◽  
The Mathematical Model ◽  
Body Theory

REVO five-axis system, designed for the orthogonal coordinate measuring machines, must be reconfigured for the application in the non-orthogonal coordinate measuring machines. First, in this article, error sources of the system and components of measurement data are analyzed; then, scale values of coordinate measuring machine axes, which are essential to derive the coordinates of measured points in non-orthogonal coordinate measuring machine, are separated out. Besides, the mathematical model of REVO is established based on the quasi-rigid body theory, from which the measurement results can be evaluated by data derived instead of that returned by the system. The effectiveness of both separation of scale values and mathematical model of REVO is proved by experiments and practice. The research of this article is of great significance to the application of REVO five-axis system in the non-orthogonal coordinate measuring machine.

Profile Voltage on One Phase Cable Channel at Every Distance 17 Meters in All 102 Meter That was 1000 Watt with Least Square Method

2019 ◽  
Vol 16 (12) ◽  
pp. 5175-5179
Author(s):  
Sofiah ◽  
Abdul Majid ◽  
Cekmas Cekdin
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Least Square Method ◽  
Equation Model ◽  
Least Square ◽  
Cable Channel ◽  
Percentage Difference ◽  
Measurement Results ◽  
The Mathematical Model

In this paper, it is discussed to determine a voltage modeling on a 102 meter one-phase cable channel which is loaded with a 1000 Watt lamp with the least square method. To obtain this method is by measuring the voltage at the points specified in the cable. After the measurement data is obtained then it is calculated to determine the mathematical model with the least square method. The least square method is a method for predicting a certain price. This method is also called the smallest quadratic method with the equation V = a + bX. With V is the measurement voltage (Volt) at distance X from the source, X distance from the source (meter), n ila a and b are calculated based on the measurement data. After the equation model is obtained, then we compare it with the measurement results. This comparison is useful to know what percentage difference between the results of the measurement and calculation.

scholarly journals The Impact of Elongation on Change in Electrical Resistance of Electrically Conductive Yarns Woven into Fabric

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3390
Author(s):  
Željko Knezić ◽  
Željko Penava ◽  
Diana Šimić Penava ◽  
Dubravko Rogale
Keyword(s):  
Mathematical Model ◽  
Electrical Resistance ◽  
Electrically Conductive ◽  
Textile Materials ◽  
Measurement Results ◽  
Conductive Yarns ◽  
Yarn Count ◽  
As Relationship ◽  
The Impact ◽  
The Mathematical Model

Electrically conductive yarns (ECYs) are gaining increasing applications in woven textile materials, especially in woven sensors suitable for incorporation into clothing. In this paper, the effect of the yarn count of ECYs woven into fabric on values of electrical resistance is analyzed. We also observe how the direction of action of elongation force, considering the position of the woven ECY, effects the change in the electrical resistance of the electrically conductive fabric. The measurements were performed on nine different samples of fabric in a plain weave, into which were woven ECYs with three different yarn counts and three different directions. Relationship curves between values of elongation forces and elongation to break, as well as relationship curves between values of electrical resistance of fabrics with ECYs and elongation, were experimentally obtained. An analytical mathematical model was also established, and analysis was conducted, which determined the models of function of connection between force and elongation, and between electrical resistance and elongation. The connection between the measurement results and the mathematical model was confirmed. The connection between the mathematical model and the experimental results enables the design of ECY properties in woven materials, especially textile force and elongation sensors.

scholarly journals Diagnostic Procedures for Jet Engines

1985 ◽  
Author(s):  
R. Lunderstädt ◽  
K. Fiedler
Keyword(s):  
Mathematical Model ◽  
Path Analysis ◽  
Working Conditions ◽  
Measurement Data ◽  
Diagnostic Procedures ◽  
Practical Significance ◽  
Jet Engines ◽  
Actual Measurement ◽  
Jet Engine ◽  
The Mathematical Model

In the paper to be presented diagnostic procedures on the basis of a gas path analysis are applied on a two-shaft jet engine. Starting from the mathematical model of the engine a filter-algorithm is used which delivers from actual measurement data the state of the engine for different working conditions. The procedure is proven for some examples and discussed in regard of its practical significance.

Statistical Analysis of the Roundness Error Data

2012 ◽  
Vol 472-475 ◽  
pp. 869-874 ◽  
Author(s):  
Zhao Peng Dong ◽  
Li Ling Huang ◽  
Hai Ting Xie ◽  
Fu Gui Huang
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Statistical Analysis ◽  
Normal Distribution ◽  
Mathematical Knowledge ◽  
Measurement Data ◽  
Roundness Error ◽  
Main Emphasis ◽  
The Mathematical Model ◽  
Roundness Measurement

In order to simulate the actual roundness measurement accurately, must find the mathematical model of the actual roundness data, the paper’s main emphasis is doing statistical analysis by plenty of measurement data of roundness, using mathematical knowledge to prove that the actual characteristics of roundness parameters obey the normal distribution, and providing the basis for subsequent computer simulation in the future

Effects of Powders on the Precision of a Powder Metallurgy Helical Gear

2007 ◽  
Author(s):  
Ming-Ta Yu ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Powder Metallurgy ◽  
Helical Gear ◽  
Precision Measurements ◽  
Manufacture Process ◽  
Measurement Results ◽  
Surface Deviations ◽  
Two Parameters ◽  
The Mathematical Model ◽  
The Relationship

This study refers to the conditions of practical powder metallurgy manufacture process, and proceeds to experiments and gear precision measurements as well as investigation on the effects of two parameters, powders and pitch circle radius, on gear precision. The relationship between gear parameters and gear surface deviations was derived from the mathematical model of the involute helical gear and the analysis of gear surface deviations. In accordance with the measurement results of experiments, an ideal correction on the parameters of a forming die is obtained from the computer simulations of gear surface deviations.

scholarly journals Measurement of Continuous Quantities and their Statistical Evaluation

2014 ◽  
Vol 44 (1) ◽  
pp. 25-32
Author(s):  
Reinhard Karl Viertl
Keyword(s):  
Mathematical Model ◽  
Statistical Analysis ◽  
Statistical Evaluation ◽  
Measurement Data ◽  
Real Numbers ◽  
Measurement Results ◽  
Continuous Quantities ◽  
Fuzzy Subsets

Measurement results of continuous quantities are always more or less imprecise. This imprecision is different from errors. The most suitable mathematical model to describe imprecision is by special fuzzy subsets of the set of real numbers R, called characterizing functions. The statistical analysis of fuzzy measurement data is subject of this paper. 

Study on Hydraulic Energy-Recovering Workover Rig and the Simulation for Lifting the Pipestring

2006 ◽  
Vol 129 (2) ◽  
pp. 96-101 ◽  
Author(s):  
Zhang Lujun
Keyword(s):  
Mathematical Model ◽  
Potential Energy ◽  
Energy Saving ◽  
Simulation Analysis ◽  
Actual Measurement ◽  
Measurement Results ◽  
Vessel Volume ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Special Working

In this paper, an advanced energy-saving petroleum machinery, the hydraulic energy-recovering workover rig, is researched. The equipped power of this rig is only one third of an ordinary rig, and this rig can also recover and reuse the potential energy which is released by the pipestring when lowered. The special working theory of this rig is introduced. An energy-saving analysis is conducted. Analysis shows that when lowering the pipestring which weighs 260kN, the energy recovered by this rig is about 240×106J. The mathematical model of lifting the pipestring is established and a simulation analysis is conducted. Through simulation, some conclusions are obtained: (1) the lighter the pipestring the shorter the pipestring lifting time; (2) the smaller the throttle valve path area the longer the pipestring lifting time; (3) the smaller the air vessel volume the shorter the pipestring lifting time. The actual measurement results prove that the simulation results are right.

Model and Parameters Identification of Non-Linear Joint by Force-State Mapping in Frequency Domain

2007 ◽  
Vol 23 (4) ◽  
pp. 367-380 ◽  
Author(s):  
J.-H. Wang ◽  
H.-Y. Huang
Keyword(s):  
Mathematical Model ◽  
Frequency Domain ◽  
Measurement Data ◽  
Optimal Model ◽  
Identification Procedure ◽  
Non Linear ◽  
Allowable Range ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Nonlinear Joints

AbstractGenerally, the Force-State Mapping (FSM) is an effective method to identify the parameters of nonlinear joints provided that the joint model is exactly known in advance. However, the variation of the non-linear joints is so large that the mathematical models of non-linear joints generally are not known in advance. Therefore, the model and the parameters of a non-linear joint should be identified simultaneously in practice. In this work, a new identification procedure which was based on the FSM method in frequency domain was proposed to identify the mathematical model and parameters of a non-linear joint simultaneously. Generally, there are many feasible combinations of models and parameters which can satisfy the measurement data within an allowable range of error. In this work, an iteration procedure was used to update the feasible models to result in an optimal model with its parameters. The simulation results show that a proper mathematical model and accurate parameters can be identified simultaneously by the new procedure even that the measurement data are contaminated by noise.

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