A Mathematical Model for Tire/Wheel Assembly Balance

1993 ◽  
Vol 21 (4) ◽  
pp. 220-231
Author(s):  
E. J. Ni
Keyword(s):  
Mathematical Model ◽  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
Monte Carlo Model ◽  
Element Model ◽  
Equation Of Motion ◽  
Rigid Body Dynamics ◽  
Production Distribution ◽  
Body Dynamics

Abstract A mathematical model is developed to calculate the weight required on a tire/wheel assembly to balance wheel nonuniformity effects such as the lateral runout. A finite element model of a tire mounted on a rigid wheel is used to simulate the free spinning about a skewed axis. The result showed that Euler's equation of motion in rigid body dynamics can be used to calculate the imbalance caused by wheel lateral runout. This equation is then used in a Monte Carlo model to simulate a production distribution. The model can be used to define tire and wheel specification limits, and to predict the number of assemblies that will have unacceptable imbalances. The verification of the model and results of the Monte Carlo simulation are presented.

Numerical and experimental investigation of the vibration of rotors with loose discs

2009 ◽  
Vol 224 (1) ◽  
pp. 85-94 ◽  
Author(s):  
M Behzad ◽  
M Asayesh
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Experimental Tests ◽  
Element Model ◽  
Equation Of Motion ◽  
Finite Element Code ◽  
Rotating Speed ◽  
Rotating Discs ◽  
Gyroscopic Effects ◽  
Measurement Location

In this study, the energy method has been used to develop a finite-element code for studying the effects of loose rotating discs on the rotor—bearing systems’ response. A mathematical model of the loose disc has resulted in terms similar to unbalance and gyroscopic effects in the equation of motion of the system. Results of this study show that rotor response and beating phenomena are a function of measurement location, loose disc mass and inertia, ratio of rotating speed to the speed of loose disc, and clearance between the loose disc and shaft considering constant speed for loose disc and shaft. The developed finite-element model can numerically give the response of rotors with any number of loose discs at any location with isotropic or orthotropic supports. Results of numerical calculation have been verified by experimental tests.

scholarly journals Voronoi diagram and Monte-Carlo simulation based finite element optimization for cost-effective 3D printing

2021 ◽  
Vol 50 ◽  
pp. 101301
Author(s):  
A.Z. Zheng ◽  
S.J. Bian ◽  
E. Chaudhry ◽  
J. Chang ◽  
H. Haron ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
3D Printing ◽  
Voronoi Diagram ◽  
Cost Effective ◽  
Simulation Based

scholarly journals Aspects of Uncertainty Analysis for Large Nonlinear Computational Models

2010 ◽  
Vol 24-25 ◽  
pp. 25-41 ◽  
Author(s):  
Keith Worden ◽  
W.E. Becker ◽  
Manuela Battipede ◽  
Cecilia Surace
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Computational Models ◽  
Element Model ◽  
Finite Element Models ◽  
Bayesian Algorithm ◽  
Basic Principles ◽  
Structure Interaction ◽  
Output Uncertainty ◽  
Input Uncertainties

This paper concerns the analysis of how uncertainty propagates through large computational models like finite element models. If a model is expensive to run, a Monte Carlo approach based on sampling over the possible model inputs will not be feasible, because the large number of model runs will be prohibitively expensive. Fortunately, an alternative to Monte Carlo is available in the form of the established Bayesian algorithm discussed here; this algorithm can provide information about uncertainty with many less model runs than Monte Carlo requires. The algorithm also provides information regarding sensitivity to the inputs i.e. the extent to which input uncertainties are responsible for output uncertainty. After describing the basic principles of the Bayesian approach, it is illustrated via two case studies: the first concerns a finite element model of a human heart valve and the second, an airship model incorporating fluid structure interaction.

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