Dynamic Modeling of a Rolling Flexible Sphere

2015 ◽  
Author(s):  
François Robert Hogan ◽  
James Richard Forbes ◽  
Alex Walsh
Keyword(s):  
Spherical Shell ◽  
Numerical Simulations ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Flat Surface ◽  
Free Vibrations ◽  
Lagrangian Formulation ◽  
Discretization Method ◽  
Motion Equations

The motion equations of a rolling flexible spherical shell are derived using a Lagrangian formulation. The motion equations developed capture the nonholonomic nature of the flexible sphere rolling without slip on a flat surface. The free vibrations of the spherical shell are modeled using the Rayleigh-Ritz discretization method. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the spherical shell on its trajectory.

Modeling of a Rolling Flexible Circular Ring

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
François Robert Hogan ◽  
James Richard Forbes
Keyword(s):  
Numerical Simulations ◽  
Dynamic Model ◽  
Lagrange Multipliers ◽  
Flat Surface ◽  
Ritz Method ◽  
Free Vibrations ◽  
Circular Ring ◽  
Ring Rolling ◽  
Motion Equations ◽  
Out Of Plane

The motion equations of a rolling flexible circular ring are derived using a Lagrangian formulation. The in-plane flexural and out-of-plane twist-bending free vibrations are modeled using the Rayleigh–Ritz method. The motion equations of a flexible circular ring translating and rotating in space are first developed and then constrained to roll on a flat surface by introducing Lagrange multipliers. The motion equations developed capture the nonholonomic nature of the circular ring rolling without slip on a flat surface. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the circular ring on its trajectory. The vibrations of the circular ring are observed to impact the ring's motion.

Modeling of a Rolling Flexible Spherical Shell

2016 ◽  
Vol 83 (9) ◽  
Author(s):  
François Robert Hogan ◽  
James Richard Forbes
Keyword(s):  
Spherical Shell ◽  
Numerical Simulations ◽  
Dynamic Model ◽  
Nonholonomic Constraint ◽  
Flat Surface ◽  
Lagrangian Approach ◽  
Martian Surface ◽  
Motion Equations ◽  
Thin Walls

The purpose of this paper is to develop the motion equations of a flexible spherical shell rolling without slip on a flat surface. The motivation for this paper stems from tumbleweed rovers, which are envisioned to roll, deform, and bounce on the Martian surface due to the flexible nature of their thin walls. The motion equations are derived using a constrained Lagrangian approach and capture the rolling without slip nonholonomic constraint. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the spherical shell on its trajectory.

Dynamic Modeling of a Quadruped With a Robotic Tail Using Virtual Work Principle

2018 ◽  
Author(s):  
Yujiong Liu ◽  
Pinhas Ben-Tzvi
Keyword(s):  
Numerical Simulations ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Virtual Work ◽  
Inverse Model ◽  
Virtual Work Principle ◽  
Alternative Approach ◽  
Systematic Methodology ◽  
Methods Numerical

For utilizing robotic tail to stabilize and maneuver a quadruped, it is important to understand the mechanism of how the tail motion influences the quadruped motion which requires obtaining an analytic dynamic model. This paper presents a systematic methodology for modeling the dynamics of a general quadruped (capable of all 6 DOF motions) with a robotic pendulum tail based on the virtual work principle. The formulation of this model is motivated by robotic tail research, it can also be used as an alternative approach to model the quadruped dynamics other than using Lagrangian and Newton-Euler based methods. Numerical simulations are also conducted to verify both the forward and the inverse model.

Dynamic Modelling of a 3DOF Medical Parallel Robot with One Decoupled Motion

2013 ◽  
Vol 837 ◽  
pp. 594-599 ◽  
Author(s):  
Mircea Neagoe ◽  
Nadia Cretescu ◽  
Radu Saulescu
Keyword(s):  
Numerical Simulations ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Lagrange Multipliers ◽  
Dynamic Modelling ◽  
Parallel Robot ◽  
Multipliers Method ◽  
Adams Software ◽  
Decoupled Motion ◽  
Analytical Dynamic

The paper presents the dynamic modeling of a 3DOF parallel robot of 1PRRR+2PRPaR type using the Lagrange multipliers method in the rigid link assumption. Numerical simulations of the analytical dynamic model, developed using Maple software, on representative trajectories are carried out and these results are finally validated trough numerical simulations in the MBS ADAMS software. Final conclusions are drawn, useful for researchers and practitioners in the robotic field.

Modeling and validation of crankshaft speed fluctuations of a single-cylinder four-stroke diesel engine

2021 ◽  
pp. 095440702110262
Author(s):  
Mustafa Babagiray ◽  
Hamit Solmaz ◽  
Duygu İpci ◽  
Fatih Aksoy
Keyword(s):  
Diesel Engine ◽  
Dynamic Model ◽  
Moment Of Inertia ◽  
Mass Motion ◽  
Cylinder Pressure ◽  
Motion Equations ◽  
Single Cylinder ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Speed Fluctuations

In this study, a dynamic model of a single-cylinder four-stroke diesel engine has been created, and the crankshaft speed fluctuations have been simulated and validated. The dynamic model of the engine consists of the motion equations of the piston, conrod, and crankshaft. Conrod motion was modeled by two translational and one angular motion equations, by considering the kinetic energy resulted from the mass moment of inertia and conrod mass. Motion equations involve in-cylinder gas pressure forces, hydrodynamic and dry friction, mass inertia moments of moving parts, starter moment, and external load moment. The In-cylinder pressure profile used in the model was obtained experimentally to increase the accuracy of the model. Pressure profiles were expressed mathematically using the Fourier series. The motion equations were solved by using the Taylor series method. The solution of the mathematical model was performed by coding in the MATLAB interface. Cyclic speed fluctuations obtained from the model were compared with experimental results and found compitable. A validated model was used to analyze the effects of in-cylinder pressure, mass moment of inertia of crankshaft and connecting rod, friction, and piston mass. In experiments for 1500, 1800, 2400, and 2700 rpm engine speeds, crankshaft speed fluctuations were observed as 12.84%, 8.04%, 5.02%, and 4.44%, respectively. In simulations performed for the same speeds, crankshaft speed fluctuations were calculated as 10.45%, 7.56%, 4.49%, and 3.65%. Besides, it was observed that the speed fluctuations decreased as the average crankshaft speed value increased. In the simulation for 157.07, 188.49, 219.91, 251.32, and 282.74 rad/s crankshaft speeds, crankshaft speed fluctuations occurred at rates of 10.45%, 7.56%, 5.84%, 4.49%, and 3.65%, respectively. The effective engine power was achieved as 5.25 kW at an average crankshaft angular speed of 219.91 rad/s. The power of friction loss in the engine was determined as 0.68 kW.

Multibody Dynamic Model of Web Guiding System With Moving Web

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Lei Yu ◽  
Zhihua Zhao ◽  
Gexue Ren
Keyword(s):  
Dynamic Model ◽  
Lateral Displacement ◽  
Dynamical Behavior ◽  
Contact Forces ◽  
Lagrangian Formulation ◽  
Pi Control ◽  
Control Law ◽  
Reference Surface ◽  
Multibody Dynamic ◽  
Guiding System

In this paper, a multibody dynamic model is established to simulate the dynamics and control of moving web with its guiding system, where the term moving web is used to describe thin materials, which are manufactured and processed in a continuous, flexible strip form. In contrast with available researches based on Eulerian description and beam assumption, webs are described by Lagrangian formulation with the absolute nodal coordinate formulation (ANCF) plate element, which is based on Kirchhoff’s assumptions that material normals to the original reference surface remain straight and normal to the deformed reference surface, and the nonlinear elasticity theory that accounts for large displacement, large rotation, and large deformation. The rollers and guiding mechanism are modeled as rigid bodies. The distributed frictional contact forces between rollers and web are considered by Hertz contact model and are evaluated by Gauss quadrature. The proportional integral (PI) control law for web guiding is also embedded in the multibody model. A series of simulations on a typical web-guide system is carried out using the multibody dynamics approach for web guiding system presented in this study. System dynamical information, for example, lateral displacement, stress distribution, and driving moment for web guiding, are obtained from simulations. Parameter sensitivity analysis illustrates the effect of influence variables and effectiveness of the PI control law for lateral movement control of web that are verified under different gains. The present Lagrangian formulation of web element, i.e., ANCF element, is not only capable of describing the large movement and deformation but also easily adapted to capture the distributed contact forces between web and rollers. The dynamical behavior of the moving web can be accurately described by a small number of ANCF thin plate elements. Simulations carried out in this paper show that the present approach is an effective method to assess the design of web guiding system with easily available desktop computers.

scholarly journals Planetary Gearbox Dynamic Modeling Considering Bearing Clearance and Sun Gear Tooth Crack

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2638
Author(s):  
Xianhua Chen ◽  
Xingkai Yang ◽  
Ming J. Zuo ◽  
Zhigang Tian
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Failure Modes ◽  
Gear Tooth ◽  
Working Environment ◽  
The Sun ◽  
Planetary Gearbox ◽  
Bearing Clearance ◽  
Vibration Responses ◽  
Planet Gear

Planetary gearbox systems are critical mechanical components in heavy machinery such as wind turbines. They may suffer from various failure modes, due to the harsh working environment. Dynamic modeling is a useful method to support early fault detection for enhancing reliability and reducing maintenance costs. However, reported studies have not considered the sun gear tooth crack and bearing clearance simultaneously to analyze their combined effect on vibration characteristics of planetary gearboxes. In this paper, a dynamic model is developed for planetary gearboxes considering the clearance of planet gear, sun gear, and carrier bearings, as well as sun gear tooth crack levels. Bearing forces are calculated considering bearing clearance, and the dynamic model equations are updated accordingly. The results reveal that the combination of bearing clearances can affect the vibration response with sun gear tooth crack by increasing the kurtosis. It is found that the effect of planet gear bearing clearance is very small, while the sun gear and carrier bearing clearance has clear impact on the vibration responses. These findings suggest that the incorporation of bearing clearance is important for planetary gearbox dynamic modeling.

Sensor Dynamic Modeling Based on LS-SVM and NGA

2008 ◽  
Vol 381-382 ◽  
pp. 439-442
Author(s):  
Qi Wang ◽  
Zhi Gang Feng ◽  
K. Shida
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Support Vector Machine ◽  
Least Squares ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Support Vector ◽  
Local Minima ◽  
Highly Nonlinear ◽  
Sharing Function

Least squares support vector machine (LS-SVM) combined with niche genetic algorithm (NGA) are proposed for nonlinear sensor dynamic modeling. Compared with neural networks, the LS-SVM can overcome the shortcomings of local minima and over fitting, and has higher generalization performance. The sharing function based niche genetic algorithm is used to select the LS-SVM parameters automatically. The effectiveness and reliability of this method are demonstrated in two examples. The results show that this approach can escape from the blindness of man-made choice of LS-SVM parameters. It is still effective even if the sensor dynamic model is highly nonlinear.

Dynamic Modeling of Planar Flexible Multi-Link Manipulators with Accounting for both Link Foreshortening and Link Material Damping

2011 ◽  
Vol 199-200 ◽  
pp. 19-24
Author(s):  
Jin Fu Zhang
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Dynamic Performance ◽  
Material Damping ◽  
Motion Responses ◽  
Case Simulation ◽  
Tip Mass ◽  
Lagrange Approach

In order to investigate dynamic performance of flexible multi-link manipulators more exactly, establishing the dynamic model with accounting for link foreshortening and link material damping is needed. In this paper, a new dynamic model for planar flexible multi-link manipulators is established by using Lagrange approach. Both link foreshortening and link material damping are accounted for in this model. As a case simulation, this model is applied to a planar flexible two-link manipulator with a tip mass, and the motion responses of the manipulator are obtained using Gear method.

System-dynamic model of power redistribution among several subjects

2021 ◽  
pp. 52-57
Author(s):  
D.S. Zhukov
Keyword(s):  
Decision Making ◽  
Simple Model ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Computer Experiments ◽  
System Dynamic ◽  
System Dynamic Model ◽  
Mathematical Apparatus ◽  
Stocks And Flows ◽  
Specialized Program

A simple model simulating the redistribution of decision-making functions between the state, business, bureaucracy and regional elites is presented. The methodological basis of the work is system-dynamic modeling. The model is implemented in the specialized program Powersim Studio 10. A diagram of stocks and flows is considered, all elements of which were compared with certain political science concepts. The mathematical apparatus of the model is described. Some results of computer experiments are presented: these results indicate the operability and interpretability of the model.

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