scholarly journals An Improved Capacitive Sensor for Detecting the Micro-Clearance of Spherical Joints

Sensors ◽  
2019 ◽  
Vol 19 (12) ◽  
pp. 2694 ◽  
Author(s):  
Wen Wang ◽  
Wenjun Qiu ◽  
He Yang ◽  
Haimei Wu ◽  
Guang Shi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Measurement Accuracy ◽  
Detection Method ◽  
Capacitive Sensor ◽  
Parallel Manipulators ◽  
Differential Capacitance ◽  
Industrial Robots ◽  
The Mathematical Model ◽  
Fringe Effect

Due to the flexible and compact structures, spherical joints are widely used in parallel manipulators and industrial robots. Real-time detection of the clearance between the ball and the socket in spherical joints is beneficial to compensate motion errors of mechanical systems and improve their transmission accuracy. This work proposes an improved capacitive sensor for detecting the micro-clearance of spherical joints. First, the structure of the capacitive sensor is proposed. Then, the mathematical model for the differential capacitance of the sensor and the eccentric micro-displacement of the ball is deduced. Finally, the capacitance values of the capacitive sensor are simulated with Ansoft Maxwell. The simulated values of the differential capacitances at different eccentric displacements agree well with the theoretical ones, indicating the feasibility of the proposed detection method. In addition, the simulated results show that the proposed capacitive sensor could effectively reduce the capacitive fringe effect, improving the measurement accuracy.

scholarly journals A Novel Method for the Micro-Clearance Measurement of a Precision Spherical Joint Based on a Spherical Differential Capacitive Sensor

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3366 ◽  
Author(s):  
Wen Wang ◽  
He Yang ◽  
Min Zhang ◽  
Zhanfeng Chen ◽  
Guang Shi ◽  
...  
Keyword(s):  
Capacitive Sensor ◽  
Differential Capacitance ◽  
Industrial Robots ◽  
Parallel Mechanisms ◽  
Spherical Joint ◽  
Compact Structure ◽  
Spacing Variation ◽  
Novel Method ◽  
The Mathematical Model ◽  
Fringe Effect

A spherical joint is a commonly used mechanical hinge with the advantages of compact structure and good flexibility, and it becomes a key component in many types of equipment, such as parallel mechanisms, industrial robots, and automobiles. Real-time detection of a precision spherical joint clearance is of great significance in analyzing the motion errors of mechanical systems and improving the transmission accuracy. This paper presents a novel method for the micro-clearance measurement with a spherical differential capacitive sensor (SDCS). First, the structure and layout of the spherical capacitive plates were designed according to the measuring principle of capacitive sensors with spacing variation. Then, the mathematical model for the spatial eccentric displacements of the ball and the differential capacitance was established. In addition, equipotential guard rings were used to attenuate the fringe effect on the measurement accuracy. Finally, a simulation with Ansoft Maxwell software was carried out to calculate the capacitance values of the spherical capacitors at different eccentric displacements. Simulation results indicated that the proposed method based on SDCS was feasible and effective for the micro-clearance measurement of the precision spherical joints with small eccentricity.

scholarly journals A Novel Approach for Detecting Rotational Angles of a Precision Spherical Joint Based on a Capacitive Sensor

Micromachines ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 280 ◽  
Author(s):  
Wen Wang ◽  
He Yang ◽  
Min Zhang ◽  
Zhanfeng Chen ◽  
Guang Shi ◽  
...  
Keyword(s):  
Real Time ◽  
Capacitive Sensor ◽  
Parallel Manipulators ◽  
Angle Measurement ◽  
Mechanical Transmission ◽  
Spherical Joint ◽  
Rotational Angle ◽  
Loop Control ◽  
Novel Approach ◽  
The Mathematical Model

Precision spherical joints are commonly employed as multiple degree-of-freedom (DOF) mechanical hinges in many engineering applications, e.g., robots and parallel manipulators. Real-time and precise measurement of the rotational angles of spherical joints is not only beneficial to the real-time and closed-loop control of mechanical transmission systems, but also is of great significance in the prediction and compensation of their motion errors. This work presents a novel approach for rotational angle measurement of spherical joints with a capacitive sensor. First, the 3-DOF angular motions of a spherical joint were analyzed. Then, the structure of the proposed capacitive sensor was presented, and the mathematical model for the rotational angles of a spherical joint and the capacitance of the capacitors was deduced. Finally, the capacitance values of the capacitors at different rotations were simulated using Ansoft Maxwell software. The simulation results show that the variation in the simulated capacitance values of the capacitors is similar to that of the theoretical values, suggesting the feasibility and effectiveness of the proposed capacitive detection method for rotational angles of spherical joints.

scholarly journals Error Analysis of a Spherical Capacitive Sensor for the Micro-Clearance Detection in Spherical Joints

Micromachines ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 837 ◽  
Author(s):  
Wen Wang ◽  
Wenjun Qiu ◽  
He Yang ◽  
Keqing Lu ◽  
Zhanfeng Chen ◽  
...  
Keyword(s):  
Error Analysis ◽  
Mathematical Models ◽  
Machine Tools ◽  
Medical Equipment ◽  
Measurement Accuracy ◽  
Capacitive Sensor ◽  
Differential Capacitance ◽  
Industrial Robots ◽  
Error Sources ◽  
Inclined Angle

Spherical joints have attracted increasing interest in the engineering applications of machine tools, industrial robots, medical equipment, and so on. As one of the promising methods of detecting the micro-clearance in spherical joints, the measurement accuracy of a spherical capacitive sensor could be affected by imperfectness during the manufacturing and installation of the sensor. This work presents error analysis of a spherical capacitive sensor with a differential structure and explores the dependence of the differential capacitance on manufacturing and the installation imperfectness. Five error sources are examined: the shape of the ball and the capacitive plate, the axial and radial offset of the plate, and the inclined installation of the plate. The mathematical models for calculating the capacitance errors of the spherical capacitive sensor are deduced and validated through a simulation using Ansoft Maxwell. The results show that the measurement accuracy of the spherical capacitive sensor is significantly affected by the shape of plates and ball, the axial offset, and the inclined angle of the plate. In contrast, the effect of the radial offset of the plate is quite small.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

A Modular Code for Real Time Dynamic Simulation of Gas Turbines in Simulink

2002 ◽  
Vol 128 (3) ◽  
pp. 506-517 ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
M. Mastrovito
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Gas Turbine ◽  
Dynamic Behavior ◽  
Gas Turbines ◽  
Simulation Software ◽  
Computational Time ◽  
High Fidelity ◽  
Time Step ◽  
The Mathematical Model

A high-fidelity real-time simulation code based on a lumped, nonlinear representation of gas turbine components is presented. The code is a general-purpose simulation software environment useful for setting up and testing control equipments. The mathematical model and the numerical procedure are specially developed in order to efficiently solve the set of algebraic and ordinary differential equations that describe the dynamic behavior of gas turbine engines. For high-fidelity purposes, the mathematical model takes into account the actual composition of the working gases and the variation of the specific heats with the temperature, including a stage-by-stage model of the air-cooled expansion. The paper presents the model and the adopted solver procedure. The code, developed in Matlab-Simulink using an object-oriented approach, is flexible and can be easily adapted to any kind of plant configuration. Simulation tests of the transients after load rejection have been carried out for a single-shaft heavy-duty gas turbine and a double-shaft aero-derivative industrial engine. Time plots of the main variables that describe the gas turbine dynamic behavior are shown and the results regarding the computational time per time step are discussed.

A High-Fidelity Real-Time Simulation Code of Gas Turbine Dynamics for Control Applications

2002 ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
M. Mastrovito
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Gas Turbine ◽  
Dynamic Behavior ◽  
Computational Time ◽  
High Fidelity ◽  
Simulation Code ◽  
Real Time Simulation ◽  
Time Simulation ◽  
The Mathematical Model

A novel high-fidelity real-time simulation code based on a lumped, non-linear representation of gas turbine components is presented. The aim of the work is to develop a general-purpose simulation code useful for setting up and testing control equipments. The mathematical model and the numerical procedure are specially developed in order to efficiently solve the set of algebraic and ordinary differential equations that describe the dynamic behavior of the gas turbine engine. The paper presents the model and the adopted solver procedure. The code, developed in Matlab-Simulink using an object-oriented approach, is flexible and can be easily adapted to any kind of plant configuration. For high-fidelity purposes, the mathematical model takes into account the actual composition of the working gases and the variation of the specific heats with the temperature, including a stage-by-stage model of the air-cooled expansion. Simulation tests of the transients after load rejection have been carried out for a single-shaft heavy-duty gas turbine and a double-shaft industrial engine. Time plots of the main variables that describe the gas turbine dynamic behavior are shown and the results regarding the computational time per time step are discussed.

scholarly journals A Multi-Objective Mathematical Model for Real-Time Employee Assignment in the Service Industry

2021 ◽  
Author(s):  
Gercek Budak ◽  
Xin Chen
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Customer Service ◽  
Service Industry ◽  
Programming Model ◽  
Manufacturing Sector ◽  
Mixed Integer ◽  
Multi Objective ◽  
Service Rates ◽  
The Mathematical Model

Abstract The American economy has shifted toward services since the 1980s. The service industry is an important part of economy and is growing quickly in the last three decades. It is more human-capital intensive than the manufacturing sector and there is a shortage of highly-skilled workforce. One solution to this problem is to improve the efficiency through optimization. Because demand in the service industry changes constantly, it is a great challenge to determine the number of employees and their tasks to improve customer service while reducing cost. This article develops a multi-objective mixed-integer linear programming model to dynamically assign employees to different workstations in real time. A case study of the model is solved in less than one second and its pareto optimal solutions determine the number of employees who are assigned to each workstation and the expected customer service times. The mathematical model is robust and provides optimal employee assignment and service rates for workstations in many situations.

Mathematical Modeling of a DC Motor With Encoder Feedback Using Real Time Simulation

2001 ◽  
Author(s):  
Kourosh Rahnamai ◽  
Brian Yanke
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Dc Motor ◽  
Actual System ◽  
Math Model ◽  
Real Time Simulation ◽  
System Parameters ◽  
Time Simulation ◽  
The Mathematical Model ◽  
Permanent Magnet Dc Motor

Abstract Real-time simulation is used to model and perform parameter identification of a dc motor with encoder feedback. Using a fast DSP board, a permanent-magnet dc motor is controlled through a proportional position feedback, while running in parallel a real-time simulation of the mathematical model of the same system. Parameters of the mathematical model are adjusted in real time, such that the error between actual system and math model are minimized. This method allows a fast and efficient method for calculating and verifying math model of a dynamic system.

Yawning Detection Based on Mouth Feature Points Curve Fitting

2012 ◽  
Vol 605-607 ◽  
pp. 2227-2231
Author(s):  
Wu Yang Ding ◽  
Ling Zhang ◽  
Yun Hua Chen
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Curve Fitting ◽  
Detection Method ◽  
Detection Algorithm ◽  
Corner Detection ◽  
Feature Points ◽  
Harris Corner ◽  
Fatigue Monitoring ◽  
Harris Corner Detection

A yawning detection method which can be used in drivers’ fatigue monitoring is proposed. To adapt to the variance in different mouth shapes and sizes, it based on mouth inner contour corner detection and curve fitting. First, the Harris corner detection algorithm was used to detect inner mouth feature points. Second, we established the open mouths’ mathematical model by curve fitting those points, calculated the degree of mouth openness using the mouth model, and generated the real-time M-curve. Third, the duration of big openness in successive images is divided into levels for further judgment. The validation results show that the method can obtain more precise mouth parameters and distinguish yawn from complex mouth activities. So the method achieves a higher level of accuracy.

Mathematical Model and Error Analysis of Coordinate Measuring Arm with Revo Revolving Body

2011 ◽  
Vol 52-54 ◽  
pp. 156-161 ◽  
Author(s):  
Lei Zhao ◽  
Shu Gui Liu
Keyword(s):  
Mathematical Model ◽  
Measurement Accuracy ◽  
System Model ◽  
Error Sources ◽  
Spherical Domain ◽  
New Type ◽  
Space Coordinate ◽  
Improving Accuracy ◽  
Revolving Body ◽  
The Mathematical Model

A new type of coordinate measuring arm with a Revo revolving body which can realize quick measuring in spherical domain has high stability, fast measuring speed and high accuracy compared with common coordinate measuring arm. We use the method of space coordinate transformation to solve the problem that the transformation matrix can’t be got from Revo body to test head by DH method, and apply DH theory to build the mathematical model of system. The system model is verified right by sketching. The error model is built and the effect of measurement accuracy from all error sources is deeply analyzed. It presents a theory foundation for further researching on improving accuracy of this new type of coordinate measuring arm.

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