Tolerance Analysis of Dynamic Equilibria in Multibody Systems Having Prescribed Rotational Motion

2007 ◽  
Author(s):  
Dong Hwan Choi ◽  
Hong Hee Yoo ◽  
Jonathan A. Wickert
Keyword(s):  
Monte Carlo ◽  
Rotational Motion ◽  
Multibody Systems ◽  
Dynamic Equilibrium ◽  
Tolerance Analysis ◽  
Computational Method ◽  
Speed Governor ◽  
Gyroscope Sensor ◽  
Power Generation Systems ◽  
Dynamic Equilibria

A general formulation for the tolerance analysis of dynamic equilibria in multibody systems having prescribed rotational motion is developed. In a state of dynamic equilibrium, a subset of generalized coordinates assume constant values, while the remaining coordinates vary and respond in time. Applications in which multibody systems exhibit dynamic equilibria include robots, spacecraft, propulsion and power generation systems, and some sensor devices. In the derived approach, manufacturing tolerances are mathematically modeled by probabilistic and statistical variables, through an analytical approach and through Monte Carlo simulation. An efficient computational method based upon direct differentiation is developed to calculate the first order sensitivity of the equilibria with respect to the design and manufacturing variables. To verify the accuracy and effectiveness of the present method, the present analytical method and the companion Monte Carlo approach are applied in examples to a rotating pendulum, a mechanical speed governor, and a model of a rate gyroscope sensor.

Dynamic Equilibrium Configurations of Multibody Systems

2014 ◽  
Vol 619 ◽  
pp. 8-12
Author(s):  
Ju Seok Kang
Keyword(s):  
Iteration Method ◽  
Multibody Systems ◽  
Equilibrium Configuration ◽  
Dynamic Equilibrium ◽  
Mechanical Systems ◽  
Railway Vehicle ◽  
Algebraic Form ◽  
Constrained Mechanical Systems ◽  
Speed Governor ◽  
Equilibrium Configurations

It is difficult to calculate dynamic equilibrium configuration in the mechanical systems, especially with the constraint conditions. In this paper, a method to calculate the dynamic equilibrium positions in the constrained mechanical systems is proposed. The accelerations of independent coordinates are derived in the algebraic form so that the numerical solution is easily obtained by the iteration method. The proposed method has been applied to calculate the dynamic equilibrium configuration for speed governor and the wheelset of railway vehicle.

On modeling and dynamics of a multiple launch rocket system

2021 ◽  
pp. 095441002098224
Author(s):  
Bo Li ◽  
Xiaoting Rui ◽  
Guoping Wang ◽  
Jianshu Zhang ◽  
Qinbo Zhou
Keyword(s):  
Monte Carlo ◽  
Multibody Systems ◽  
Euler Method ◽  
Dynamics Analysis ◽  
Analysis Problem ◽  
Dynamic Design ◽  
Proposed Model ◽  
And Control ◽  
Rocket System ◽  
Complete Process

Dynamics analysis is currently a key technique to fully understand the dynamic characteristics of sophisticated mechanical systems because it is a prerequisite for dynamic design and control studies. In this study, a dynamics analysis problem for a multiple launch rocket system (MLRS) is developed. We particularly focus on the deductions of equations governing the motion of the MLRS without rockets by using a transfer matrix method for multibody systems and the motion of rockets via the Newton–Euler method. By combining the two equations, the differential equations of the MLRS are obtained. The complete process of the rockets’ ignition, movement in the barrels, airborne flight, and landing is numerically simulated via the Monte Carlo stochastic method. An experiment is implemented to validate the proposed model and the corresponding numerical results.

scholarly journals Monte Carlo ice flow modeling projects a new stable configuration for Columbia Glacier, Alaska, by c. 2020

2012 ◽  
Vol 6 (2) ◽  
pp. 893-930 ◽  
Author(s):  
W. Colgan ◽  
W. T. Pfeffer ◽  
H. Rajaram ◽  
W. Abdalati
Keyword(s):  
Monte Carlo ◽  
Dynamic Equilibrium ◽  
Stable Configuration ◽  
Ice Flow ◽  
Wide Range ◽  
Ensemble Mean ◽  
Iceberg Calving ◽  
Calving Rate ◽  
Parameter Values

Abstract. Due to the abundance of observational datasets collected since the onset of its retreat (c. 1983), Columbia Glacier, Alaska, provides an exciting modeling target. We perform Monte Carlo simulations of the form and flow of Columbia Glacier, using a 1-D (depth-integrated) flowline model, over a wide range of parameter values and forcings. An ensemble filter is imposed following spin-up to ensure that only simulations which accurately reproduce observed pre-retreat glacier geometry are retained; all other simulations are discarded. The selected ensemble of simulations reasonably reproduces numerous highly transient post-retreat observed datasets with a minimum of parameterizations. The selected ensemble mean projection suggests that Columbia Glacier will achieve a new dynamic equilibrium (i.e. "stable") ice geometry c. 2020, by which time iceberg calving rate will have returned to approximately pre-retreat values. Comparison of the observed 1957 and 2007 glacier geometries with the projected 2100 glacier geometry suggests that, by 2007, Columbia Glacier had already discharged ∼83 % of its total sea level rise contribution expected by 2100. This case study therefore highlights the difficulties associated with the future extrapolation of observed glacier mass loss rates that are dominated by iceberg calving.

scholarly journals Dynamic Equilibria in Statistical and Nonlinear Physics of Uniform Stress Rotating Space Elevators (USRSE)

2019 ◽  
Vol 11 (6) ◽  
pp. 56
Author(s):  
Leonardo Golubovic ◽  
Steven Knudsen
Keyword(s):  
Carbon Nanotubes ◽  
Materials Science ◽  
Dynamic Equilibrium ◽  
Outer Space ◽  
Point Of View ◽  
Uniform Stress ◽  
The Earth ◽  
Equilibrium Configurations ◽  
Space Elevators ◽  
Dynamic Equilibria

The discovery of ultra-strong materials such as carbon nanotubes and diamond nano-thread structures has recently motivated an enhanced interest for the physics of Space Elevators connecting the Earth with outer space. A new concept has recently emerged in space elevator physics: Rotating Space Elevators (RSE) [Golubović, L. & Knudsen, S. (2009). Classical and statistical mechanics of celestial scale spinning strings: Rotating space elevators. Europhysics Letters 86(3), 34001.]. Objects sliding along rotating RSE string (sliding climbers) do not require internal engines or propulsion to be transported from the Earth's surface into outer space. Here we address the physics of a special RSE family, Uniform Stress Rotating Space Elevators (USRSE), characterized by constant tensile stress along the string. From the point of view of materials science, this condition provides the best control of string’s global integrity. We introduce an advanced analytic approach to obtain the dynamic equilibrium configurations of USRSE strings. We use our results to discuss the applications of USRSE for spacecraft launching.

Computational method in electrostatics based on Monte Carlo energy minimisation

2001 ◽  
Vol 148 (3) ◽  
pp. 121-124 ◽  
Author(s):  
M. Sancho ◽  
J.M. Miranda ◽  
J.L. Sebastián ◽  
S. Muñoz
Keyword(s):  
Monte Carlo ◽  
Computational Method ◽  
Energy Minimisation

Comparison of Assembly Tolerance Analysis by the Direct Linearization and Modified Monte Carlo Simulation Methods

1995 ◽  
Author(s):  
Jinsong Gao ◽  
Kenneth W. Chase ◽  
Spencer P. Magleby
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Closed Loop ◽  
Great Influence ◽  
Tolerance Analysis ◽  
Linearization Method ◽  
Direct Linearization ◽  
Highly Nonlinear ◽  
Assembly Features ◽  
Assembly Constraints

Abstract Two methods for performing statistical tolerance analysis of mechanical assemblies are compared: the Direct Linearization Method (DLM), and Monte Carlo simulation. A selection of 2-D and 3-D vector models of assemblies were analyzed, including problems with closed loop assembly constraints. Closed vector loops describe the small kinematic adjustments that occur at assembly time. Open loops describe critical clearances or other assembly features. The DLM uses linearized assembly constraints and matrix algebra to estimate the variations of the assembly or kinematic variables, and to predict assembly rejects. A modified Monte Carlo simulation, employing an iterative technique for closed loop assemblies, was applied to the same problem set. The results of the comparison show that the DLM is accurate if the tolerances are relatively small compared to the nominal dimensions of the components, and the assembly functions are not highly nonlinear. Sample size is shown to have great influence on the accuracy of Monte Carlo simulation.

Sensitivity Analysis of Dynamic Equilibrium Positions in Multibody Systems Undergoing Prescribed Rotational Motions

2007 ◽  
Author(s):  
Dong Hwan Choi ◽  
Hong Hee Yoo ◽  
Jonathan A. Wickert
Keyword(s):  
Finite Difference ◽  
Multibody Systems ◽  
Present Method ◽  
Dynamic Equilibrium ◽  
Step Size ◽  
Sensors And Actuators ◽  
Design Variables ◽  
Dynamic Equilibrium State ◽  
Rotational Motions ◽  
Engineered Systems

Multibody systems that undergo a prescribed rotational motion arise in such engineered systems as robots, spacecraft, propulsion and power generation systems, and certain sensors and actuators. The sensitivity of the system’s response to changes in the design variables is important for optimization and trade-off studies, as well as for understanding the implications of manufacturing tolerances. A general formulation is developed for analytically calculating the first-order design sensitivities of coordinate values for a multibody system’s dynamic equilibrium state during prescribed rotational motions. The method is based upon the use of relative coordinates, and a velocity transformation technique, and it is applicable to multibody systems having open or closed loop configurations. To illustrate effectiveness, accuracy, and computational efficiency, the present method is applied in three examples, and the sensitivities obtained analytically are compared with those obtained by the standard finite difference method. The finite difference approach is particularly sensitive to the choice of step size near a critical speed, and its implementation is generally more costly that the present method. In particular, there is a zero-sensitivity point at which the equilibrium configuration is insensitive to small perturbations in the design parameter’s value. That condition can be a useful design point to the extent that manufacturing tolerance and variation in design parameter’s values have no effect on dynamic equilibrium positions.

scholarly journals Sorption, Structure and Dynamics of CO2 and Ethane in Silicalite at High Pressure: A Combined Monte Carlo and Molecular Dynamics Simulation Study

Molecules ◽  
2018 ◽  
Vol 24 (1) ◽  
pp. 99 ◽  
Author(s):  
Siddharth Gautam ◽  
Tingting Liu ◽  
David Cole
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Time Scales ◽  
Rotational Motion ◽  
High Pressures ◽  
Sorption Isotherms ◽  
Md Simulations ◽  
Dynamics Simulation ◽  
Structure And Dynamics ◽  
Low Pressures

Silicalite is an important nanoporous material that finds applications in several industries, including gas separation and catalysis. While the sorption, structure, and dynamics of several molecules confined in the pores of silicalite have been reported, most of these studies have been restricted to low pressures. Here we report a comparative study of sorption, structure, and dynamics of CO2 and ethane in silicalite at high pressures (up to 100 bar) using a combination of Monte Carlo (MC) and molecular dynamics (MD) simulations. The behavior of the two fluids is studied in terms of the simulated sorption isotherms, the positional and orientational distribution of sorbed molecules in silicalite, and their translational diffusion, vibrational spectra, and rotational motion. Both CO2 and ethane are found to exhibit orientational ordering in silicalite pores; however, at high pressures, while CO2 prefers to reside in the channel intersections, ethane molecules reside mostly in the sinusoidal channels. While CO2 exhibits a higher self-diffusion coefficient than ethane at low pressures, at high pressures, it becomes slower than ethane. Both CO2 and ethane exhibit rotational motion at two time scales. At both time scales, the rotational motion of ethane is faster. The differences observed here in the behavior of CO2 and ethane in silicalite pores can be seen as a consequence of an interplay of the kinetic diameter of the two molecules and the quadrupole moment of CO2.

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