The Mechanics of Spiral Springs and Its Application in Timekeeping

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
Longhan Xie ◽  
Puihang Ko ◽  
Ruxu Du
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Critical Parameter ◽  
Dynamic Deformation ◽  
Dynamic Performance ◽  
Spiral Spring ◽  
Simulation Results ◽  
Experimental Validations ◽  
The Mathematical Model ◽  
Castigliano’S Theorem

Spiral spring is widely used in mechanisms, such as mechanical watch movements and clocks where the spiral spring is used for timekeeping. According to literature, there are only a few studies on spiral springs. In this paper, the mechanics of spiral springs is analyzed in details, and its dynamic performance in mechanical watch movements is further studied to find out its natural frequency, which is the most critical parameter for mechanical watch movements. Based on Castigliano's theorem, the mathematical model of dynamic deformation and natural frequency of the spiral spring under external axial torque is developed, and computer simulation with Matlab® is also conducted. Experimental validations are carried out, which confirm the simulation results. Experiments show that the analytical method in this paper can be used to guide and facilitate the design of spiral spring.

Simulation Technologies for Tamper System of Asphalt-Paver Based on AMESim

2010 ◽  
Vol 129-131 ◽  
pp. 1098-1103 ◽  
Author(s):  
Tian Hong Luo ◽  
Xin Fu Gan ◽  
Wen Jun Luo
Keyword(s):  
Mathematical Model ◽  
Simulation Model ◽  
Pid Controller ◽  
Dynamic Performance ◽  
Operating Principle ◽  
Simulation Results ◽  
The Stability ◽  
The Mathematical Model

Tamper mechanism is one of the most important parts in all of Asphalt-pavers. In this article, the mathematical model of the tamper system has been established and the stability of the system has been analyzed by using Matlab. According to the operating principle of tamper system of Asphalt-paver, the simulation model of tamper system of Asphalt-paver has been established by using AMESim. The main parameters of the model were set, and then, the simulation results were analyzed, which show that the system is stable and the dynamic performance of system will be improved, when accumulator and PID controller were equipped. Besides, the tamping frequency of hammer is very important to the performance of system. When tamping frequency of hammer over 20HZ, the performance of system will go bad.

Modeling Study of Long-Stroke Valve-Controlled Asymmetrical Cylinder

2011 ◽  
Vol 52-54 ◽  
pp. 291-296 ◽  
Author(s):  
Zhi Quan Xiao
Keyword(s):  
Mathematical Model ◽  
Dynamic Performance ◽  
Load Flow ◽  
Load Pressure ◽  
Simulation Results ◽  
Long Stroke ◽  
The Mathematical Model ◽  
Volume Functions ◽  
Modeling Study

With the consideration of compressibility flow and the redefined load flow and load pressure, the mathematical model of long-stroke valve-controlled asymmetrical cylinder system is presented. The equivalent volume functions, the functions of equivalent volume functions of cylinder's two chambers are introduced, which reflects the influence of piston's positions in its long stroke on the dynamic performance of valve-controlled cylinder. Simulation results show that there exists obvious differences between forward and backward directions of long-stroke valve-controlled asymmetrical cylinder system, and its dynamic performance varies along the whole stroke, where the middle-stroke position may not always be the so-called most dangerous position.

Research on Dynamic Balance Method of Precision Centrifuge

2014 ◽  
Vol 945-949 ◽  
pp. 777-780
Author(s):  
Tao Liu ◽  
Yong Xu ◽  
Bo Yuan Mao
Keyword(s):  
Mathematical Model ◽  
Balance Control ◽  
Dynamic Balance ◽  
Dynamic Balancing ◽  
Structure Characteristics ◽  
Balance System ◽  
Simulation Results ◽  
Set Up ◽  
System Controller ◽  
The Mathematical Model

Firstly, according to the structure characteristics of precision centrifuge, the mathematical model of its dynamic balancing system was set up, and the dynamic balancing scheme of double test surfaces, double emendation surfaces were established. Then the dynamic balance system controller of precision centrifuge was designed. Simulation results show that the controller designed can completely meet the requirements of precision centrifuge dynamic balance control system.

The Impact Analysis of Revolute Pair Clearance to the End Pose Accuracy of Welding Robot

2015 ◽  
Vol 778 ◽  
pp. 259-263
Author(s):  
Fa Jun Zhang ◽  
Lin Zi Li ◽  
Hui Lin ◽  
Yin Lin Pu ◽  
Zhu Xin
Keyword(s):  
Mathematical Model ◽  
Impact Analysis ◽  
Joint Clearance ◽  
Welding Robot ◽  
Movement Characteristic ◽  
Movement Stability ◽  
Simulation Results ◽  
The Impact ◽  
The Mathematical Model ◽  
Welding Position

Various uncertain factors affect the movement of the welding robot, thus welding gun tend to deviate from the theory of welding position which reduces the welding accuracy, of which the revolute pair clearance have an greater effect on the movement of the welding robot. In order to study the influence of revolute pair clearance to the end pose accuracy of welding robot, the mathematical model of revolute pair clearance was established, and the software SolidWorks was used for establishing the welding robot model, making simulations of the mechanical arm with joint clearance and no joint clearance. At last, the movement characteristic of the hinge shaft is attained. The simulation results showed that the shaft velocity and displacement of mechanical arm with joint clearance has a certain degree of fluctuation, which affecting the end pose accuracy of welding robot , and reducing the movement stability and the welding accuracy of welding robot.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

Deep and Shallow Water Low-Speed Maneuvering Tests: Comparison Between Experimental and Simulation Results

2016 ◽  
Author(s):  
Felipe Ribolla Masetti ◽  
Pedro Cardozo de Mello ◽  
Guilherme F. Rosetti ◽  
Eduardo A. Tannuri
Keyword(s):  
Mathematical Model ◽  
Small Scale ◽  
Shallow Waters ◽  
Hydrodynamic Coefficients ◽  
Low Speed ◽  
Tunnel Model ◽  
Oceanographic Research ◽  
Simulation Results ◽  
The University ◽  
The Mathematical Model

This paper presents small-scale low-speed maneuvering tests with an oceanographic research vessel and the comparison with mathematical model using the real time maneuvering simulator developed by the University of São Paulo (USP). The tests are intended to verify the behavior of the vessel and the mathematical model under transient and low speed tests. The small-scale tests were conducted in deep and shallow waters, with a depth-draft ratio equal to 1.28, in order to verify the simulator ability to represent the vessel maneuverability on both depth conditions. The hydrodynamic coefficients used in the simulator model were obtained by CFD calculations and wind tunnel model tests carried out for this vessel. Standard turning circle and accelerating turn maneuvers were used to compare the experimental and numerical results. A fair agreement was achieved for shallow and deep water. Some differences were observed mainly in the initial phase of the accelerating turn test.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

scholarly journals Hybrid Secondary Suspension Systems

2009 ◽  
Vol 16 (5) ◽  
pp. 467-480 ◽  
Author(s):  
Nader Vahdati ◽  
Mehdi Ahmadian
Keyword(s):  
Mathematical Model ◽  
Vibration Absorbers ◽  
Simple Mathematical Model ◽  
System Behavior ◽  
Engine Mounts ◽  
Suspension Systems ◽  
Tuned Vibration Absorbers ◽  
Simulation Results ◽  
Secondary Suspension ◽  
The Mathematical Model

Passive fluid mounts are used in the fixed wing applications as engine mounts. The passive fluid mount is placed in between the engine and the fuselage to reduce the cabin's structure- borne noise and vibration generated by the engine.To investigate the benefits of passive fluid mounts used in conjunction with tuned vibration absorbers (TVA), a simple mathematical model is developed. This mathematical model includes the mathematical model of a passive fluid mount, a TVA, and a spring representing the fuselage structure. The simulation results indicate that when passive fluid mounts are used in conjunction with TVAs, an active suspension system behavior is nearly created.

Mathematical model of the artificial muscle with two actuators

2020 ◽  
pp. 095440622094156
Author(s):  
Ljubinko B Kevac ◽  
Mirjana M Filipovic ◽  
Ana M Djuric
Keyword(s):  
Mathematical Model ◽  
Control Structure ◽  
Artificial Muscle ◽  
Parallel Robot ◽  
Simulation Results ◽  
Proportional Derivative Controller ◽  
Definition Of ◽  
The Mathematical Model ◽  
The Given ◽  
Very High

Characteristic construction of cable-suspended parallel robot of artificial muscle, which presents an artificial forearm, is analyzed and synthesized. Novel results were achieved and presented. Results presented in this paper were initially driven to recognize and mathematically define undefined geometric relations of the artificial forearm since it was found that they strongly affect the dynamic response of this system. It gets more complicated when one has more complex system, which uses more artificial muscle subsystems, since these subsystems couple and system becomes more unstable. Unmodeled or insufficiently modeled dynamics can strongly affect the system’s instability. Because of that, the construction of this system and its new mathematical model are defined and presented in this paper. Generally, it can be said that the analysis of geometry of selected mechanism is the first step and very important step to establish the structural stability of these systems. This system is driven with two actuators, which need to work in a coordinated fashion. The aim of this paper is to show the importance of the geometry of this solution, which then strongly affects the system’s kinematics and dynamics. To determine the complexity of this system, it was presumed that system has rigid cables. Idea is to show the importance of good defined geometry of the system, which gives good basis for the definition of mathematical model of the system. Novel program package AMCO, artificial muscle contribution, was defined for the validation of the mathematical model of the system and for choice of its parameters. Sensitivity of the system to certain parameters is very high and hence analysis of this system needs to be done with a lot of caution. Some parameters are very influential on the possible implementation of the given task of the system. Only after choosing the parameters and checking the system through certain simulation results, control structure can be defined. In this paper, proportional–derivative controller was chosen.

Intelligent Generating Examination Paper from Item Bank Based on Improved Genetic Algorithm

2014 ◽  
Vol 926-930 ◽  
pp. 3637-3640
Author(s):  
Li Feng ◽  
Qian Wu ◽  
Jing Shao Zhang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Computational Study ◽  
Item Bank ◽  
Test Paper ◽  
Improved Genetic Algorithm ◽  
Fitness Evaluation ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Examination Paper

In this paper, we analyze the disadvantage of common generating test paper algorithm. An improved genetic algorithm (IGA) is proposed and used in auto-generating examination paper algorithm. We design the mathematical model of auto-generating test paper algorithm and improved the traditional GA fitness evaluation form. A computational study is carried out to verify the algorithm. Simulation results demonstrate that the performance of IGA can work efficiently than traditional ones.

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