Stiffness Study of a Parallel Link Robot Crane for Shipbuilding Applications

1989 ◽  
Vol 111 (3) ◽  
pp. 183-193 ◽  
Author(s):  
N. G. Dagalakis ◽  
J. S. Albus ◽  
B.-L. Wang ◽  
J. Unger ◽  
J. D. Lee
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Stiffness Matrix ◽  
Main Part ◽  
Laboratory Model ◽  
Stiffness Measurement ◽  
Parallel Link ◽  
Stiffness Characteristics ◽  
External Loads ◽  
Theoretical Results

This describes the first phase of an effort to develop a robot crane for shipbuilding applications. The focus of this phase is on the study of the stiffness characteristics of this robot as a function of its geometry payload and height. A brief description of the design of the main part of the robot crane consisting of a six-wire parallel link manipulator is given. The stiffness of the manipulator to side loads and moments was studied. The nonlinear and linearized mathematical model of the manipulator stiffness matrix is derived. Stiffness measurement tests were conducted using a small size laboratory model. The results of these tests for various external loads, heights, and payloads are given. Computer simulation and theoretical results are also discussed.

Stiffness characteristics of crossed roller bearings with roller roundness deformation

2021 ◽  
pp. 1-23
Author(s):  
Van-Canh Tong ◽  
Seong-Wook Hong
Keyword(s):  
Stiffness Matrix ◽  
Load Distribution ◽  
Misalignment Angle ◽  
Angular Misalignment ◽  
Internal Load ◽  
Roller Bearings ◽  
Bearing Stiffness ◽  
Axial Clearance ◽  
Stiffness Characteristics ◽  
External Loads

Abstract This study investigated the stiffness characteristics of crossed-roller bearings (XRBs) subjected to various loading and boundary conditions. A five degree-of-freedom XRB model was adopted that considers the effect of roller roundness deformation, which was developed by the authors in a prior study. The analytical formulation for a fully occupied (5 × 5) stiffness matrix of XRB was obtained. Extended simulations were performed to determine the XRB stiffness and internal load distribution considering the effects of the external loads, axial preloads, axial clearance, and angular misalignment. The numerical results confirmed that the bearing stiffness possessed significant nonlinearity with respect to the external loads. Increasing the axial clearance reduced the stiffness of the bearing under radial and moment loading, but it did not affect the stiffness of the pure axially loaded bearing. The stiffness of the bearing with axial clearance increased consistently with the misalignment angle. The stiffness behavior of the preloaded bearing depended on the misalignment angle.

Computer Simulation of the Response of Amperometric Biosensors in Stirred and non Stirred Solution

2003 ◽  
Vol 8 (1) ◽  
pp. 3-18 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Finite Difference ◽  
Mass Transport ◽  
Enzyme Reaction ◽  
Analyte Concentration ◽  
Amperometric Biosensors ◽  
Finite Difference Technique ◽  
Enzyme Layer ◽  
Biosensor Response

A mathematical model of amperometric biosensors has been developed to simulate the biosensor response in stirred as well as non stirred solution. The model involves three regions: the enzyme layer where enzyme reaction as well as mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region, where the analyte concentration is maintained constant. Using computer simulation the influence of the thickness of the enzyme layer as well the diffusion one on the biosensor response was investigated. The computer simulation was carried out using the finite difference technique.

In-Plane Bending and Shear Deformation of Belt Contributions on Tire Cornering Stiffness Characteristics

2020 ◽  
Author(s):  
Gibin Gil ◽  
Sujin Lee
Keyword(s):  
Mathematical Model ◽  
Shear Deformation ◽  
Beam Theory ◽  
Slip Angle ◽  
Wear Properties ◽  
Angle Change ◽  
Foundation Model ◽  
Plane Bending ◽  
Stiffness Characteristics ◽  
Brush Model

ABSTRACT In radial tires, belt structure plays a role of minimizing the lateral deflection of carcass, which has a significant influence on the cornering and wear properties of a tire. The deflection of carcass affects the magnitude of tread block deformation when the tire is under the slip angle. As a result, it can change the cornering stiffness characteristics of the tire, especially when the vertical load is high. During tire development, a tire design engineer tries to find the optimal belt ply angle that satisfies the various performance requirements simultaneously, but it is not an easy task because the effect of belt angle change is different depending on the size of the tire. There have been many attempts to construct a mathematical model that represents the structural properties of the belt package, including the string-based model and the beam on elastic foundation model. But, in many cases, only the in-plane bending of belt is considered and the shear deformation is not taken into consideration. In this study, the effect of belt angle change on belt stiffness is analyzed using a mathematical model based on the Timoshenko beam theory. This model can account for the in-plane bending and shear deformation of the belt structure at the same time. The results of the analysis show how the contribution of bending and shear is changed depending on a tire design parameter, herein the belt cord angle. The effect of belt ply angle change on cornering stiffness is investigated by means of the brush model including belt flexibility. The prediction by the brush model is compared with the measurement using a Flat-trac machine, and the validity of the model is discussed.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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.

Study of the Stiffness Matrix of Preloaded Duplex Angular Contact Ball Bearings

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Shengye Lin ◽  
Shuyun Jiang
Keyword(s):  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Fixed Position ◽  
Angular Contact Ball Bearing ◽  
Face To Face ◽  
Radial Stiffness ◽  
Proposed Model ◽  
Stiffness Characteristics

This paper studies the stiffness characteristics of preloaded duplex angular contact ball bearings. First, a five degrees-of-freedom (5DOF) quasi-static model of the preloaded duplex angular contact ball bearing is established based on the Jones bearing model. Three bearing configurations (face-to-face, back-to-back, and tandem arrangements) and two preload mechanisms (constant pressure preload and fixed position preload) are included in the proposed model. Subsequently, the five-dimensional stiffness matrix of the preloaded duplex angular contact ball bearing is derived analytically. Then, an experimental setup is developed to measure the radial stiffness and the angular stiffness of duplex angular contact ball bearings. The simulated results match well with those from experiments, which prove the validity of the proposed model. Finally, the effects of bearing configuration, preload mechanism, and unloaded contact angle on the angular stiffness and the cross-coupling are studied systematically.

scholarly journals Mathematical Model of Vane Compressors for Computer Simulation of Automotive Air Conditioning Cycle.

1995 ◽  
Vol 38 (2) ◽  
pp. 199-205 ◽  
Author(s):  
Mitsuhiro Fukuta ◽  
Tadashi Yanagisawa ◽  
Takashi Shimizu ◽  
Yasuhiro Suzuki
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Air Conditioning ◽  
Automotive Air Conditioning

scholarly journals Three-dimensional computer simulation of twill woven fabric by using polynomial mathematical model

2019 ◽  
Vol 12 (4-5) ◽  
pp. 1167-1178
Author(s):  
Fang Qin ◽  
◽  
Ying Jiang ◽  
Ping Gu ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Three Dimensional ◽  
Woven Fabric

scholarly journals Bondgraph modelling and simulation of the dynamic behaviour of above-knee prostheses

1987 ◽  
Vol 11 (2) ◽  
pp. 65-70 ◽  
Author(s):  
P. G. Van De Veen ◽  
W. Van Der Tempel ◽  
J. De Vreiss
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Mass Distribution ◽  
Total Mass ◽  
Dynamic Behaviour ◽  
Step Length ◽  
Swing Phase ◽  
Knee Prostheses ◽  
Prosthetic Foot ◽  
Walking Velocity

A mathematical model was used to investigate the dynamic behaviour of an above-knee (AK) prosthesis in the swing phase and to analyse the influence of mass and mass distribution on the maximal stump load and the required energy. The model consists of a bondgraph model of the prosthesis and a “walking” model which predicts the walking velocity, step length and the femoral trajectory. Equipment was developed to measure the inertial properties of the components of the prosthesis. Through computer simulation, stickdiagrams of the swing phase and graphs of the variation with time of the hip and stump forces were obtained. It was found that for a normal AK prosthesis with a knee-lock mechanism the axial stump load is greatest at the beginning and at the end of the swing phase. At a walking velocity of 5 km/hr the maximum axial stump load amounts to 2.1 times the static weight of the prosthesis. The maximum axial stump force appeared to be almost directly proportional to the total mass of the prosthesis but independent of the mass distribution. The required energy also increased with the mass of the prosthesis but is' dependent on mass distribution. Because of their comparable weights the influence of the shoe is almost equal to the influence of the prosthetic foot. Thus lightweight shoes should be used with lightweight prosthetic feet in order to add to their advantages.

scholarly journals Modeling and Simulation in Engineering Modeling of the Electrocoagulation Processes in Nonisothermal Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Andrii Safonyk ◽  
Olena Prysiazhniuk
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Asymptotic Approximation ◽  
Iron Concentration ◽  
Current Strength ◽  
Target Component ◽  
Incompressible Fluid Flow ◽  
Electrocoagulation Process ◽  
Engineering Modeling ◽  
Nonisothermal Conditions

The paper suggests an approach to modeling the electrocoagulation process that is based on the generalization of the equations of incompressible fluid flow in nonisothermal conditions. In the model was taking into account the ratio between the values of the parameters which characterize the domination of convective and mass-exchange components of the process over diffusion. An asymptotic approximation of solutions of corresponding boundary value problems is constructed. Based on the received solutions, we conducted a computer simulation of the process of distribution of iron concentration inside the reactor that allows predicting various hydrodynamic phenomena such as internal recirculation and dead zones that affect the formation of a coagulant. The influence of current strength on the concentration of the target component at the exit from the reactor was investigated using the developed mathematical model. In addition, our findings also show the effect of the rate of heat formation from the electrodes on the efficiency of obtaining of coagulant.

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