An improved dynamic modeling approach of aerostatic thrust bearing considering frequency-varying stiffness and damping of air film

2021 ◽  
pp. 1-42
Author(s):  
Hui Zhuang ◽  
Jianguo Ding ◽  
Peng Chen ◽  
Yu Chang ◽  
Xiaoyun Zeng ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Modeling ◽  
Vibration Analysis ◽  
Thrust Bearing ◽  
Spring Model ◽  
Modeling Approach ◽  
Mass Spring Model ◽  
Mass Spring ◽  
Stiffness And Damping ◽  
Air Film

Abstract The damped mass-spring model is often employed for the dynamic modeling and vibration analysis of aerostatic bearing systems by taking the air film as equivalent springs. However, the stiffness and damping of the air film are frequency-dependent, making the commonly used approach of taking static stiffness or fixed value as the spring coefficient no longer applicable for a bearing subject to a complex external force containing different frequencies. To address this issue, this paper develops the damped mass-spring model for the aerostatic thrust bearing considering the frequency-varying stiffness and damping by means of the linear superposition method. It indicates that the air bearing is still a linear system despite the frequency-dependent character of dynamic coefficients because the bearing vibration satisfies the superposition principle. The improved dynamic modeling approach is able to accurately and efficiently predict the overall dynamic response of the thrust plate when the it is subjected to a multi-frequency vibration. In solving the overall dynamic response, the stiffness and damping associated with the responses of the transient part and steady part correspond to the natural vibration frequency and external disturbance frequencies, respectively. The feasibility and accuracy of the improved modeling approach are partly or completely verified by the direct trajectory calculation method, the CFD dynamic mesh simulation and a modal test. The proposed modeling method provides an effective way for the vibration analysis of air bearings, and in the meantime avoids the possible numerical errors caused by the traditional modeling approach.

A Simple Vibration Analysis for Running Boards and Other Attached Components

2004 ◽  
Author(s):  
Shaun Richmond
Keyword(s):  
Vibration Analysis ◽  
Spring Model ◽  
Analysis Method ◽  
Simple Analysis ◽  
Car Body ◽  
Mass Spring Model ◽  
Frequency Components ◽  
Simple Mass ◽  
Wheel Flat ◽  
Mass Spring

Vibration of attached components such as running boards, hand grabs, brake components, etc. has become a serious problem. This paper sets out a simple analysis method for ensuring the survival of these components. A simple mass spring model is used to develop a transfer function into the car body. The frequency components of a wheel flat and 39/33 foot jointed track are then established and the excitation amplitudes for components attached to the car body calculated. The response of these components at their natural frequency is then used to calculate their resulting stress levels. Simple methods for performing this analysis are described

A Simple Dynamic Model for Beams Subjected to Blast Loads

2012 ◽  
Vol 479-481 ◽  
pp. 1763-1767
Author(s):  
Z.N. Yin
Keyword(s):  
Dynamic Response ◽  
Deformation Behavior ◽  
Spring Model ◽  
Blast Loads ◽  
Lumped Mass ◽  
Proposed Model ◽  
Mass Spring Model ◽  
Three Degree Of Freedom ◽  
Mass Spring ◽  
The Relationship

A three Degree-of-Freedom (DoF) mass-spring model is proposed to predict the dynamic response of clamped supported beams subjected to blast loads at the mid-span of the beam. The stiffness of inelastic spring is defined from the relationship between force and mid-span displacement of beams subjected to blast loads. The lumped mass is calculated from the equivalency between the model and beam based on the fundamental frequency. Clamped supported solid beams and T-beams are taken as typical examples to verify the proposed model. And the influence of geometric parameters on deformation behavior is discussed in details.

One-Dimensional Analysis on the Dynamic Response of Cellular Chains to Pulse Loading

2006 ◽  
Vol 220 (5) ◽  
pp. 679-689 ◽  
Author(s):  
Z. Y. Gao ◽  
T. X. Yu
Keyword(s):  
Dynamic Response ◽  
Elastic Wave ◽  
Deformation Characteristic ◽  
Cell Number ◽  
Pulse Loading ◽  
Plastic Collapse ◽  
Spring Model ◽  
One Dimensional ◽  
Mass Spring Model ◽  
Mass Spring

On the basis of our previous studies of a typical type II structure (i.e. a pair of prebent plates), a simplified one-dimensional mass-spring model is proposed to describe the uniaxial load-deformation characteristic of cellular materials and structures. When compared with the previous mass-spring model proposed by Shim et al., the present model employs fewer parameters (only two) to describe elastic-plastic behaviour, and the structural hardening/softening is represented by only one of the parameters. The model is then used to study the dynamic response of a cellular chain to a pulse loading of specified force intensity and duration. By adjusting the value of a single parameter adopted in the model, each cell of the cellular chain is identically assigned to possess either an elastic-hardening or an elastic-softening-consolidation property. The effects of material elasticity, cell compliance characteristic, cell number, and pulse intensity and duration are all examined by this model and discussed in detail. A special attention is paid to the initiation and propagation of the plastic collapse of the cells in the cellular chain so as to identify the governing parameters. Apart from the elastic wave speed, two other characteristic velocities, i.e. the particle velocity induced by the elastic wave and the plastic collapse propagation velocity, are defined and analytically evaluated. It is found that these three characteristic velocities completely govern the elastic and plastic dynamic behaviour of the cellular chains.

scholarly journals Review on the 3-D simulation for weft knitted fabric

2021 ◽  
Vol 16 ◽  
pp. 155892502110125
Author(s):  
Sha Sha ◽  
Anqi Geng ◽  
Yuqin Gao ◽  
Bin Li ◽  
Xuewei Jiang ◽  
...  
Keyword(s):  
Physical Models ◽  
Spring Model ◽  
Finite Element Analyses ◽  
Knitted Fabrics ◽  
Piecewise Function ◽  
Fabric Structure ◽  
Weft Knitted Fabric ◽  
Mass Spring Model ◽  
Virtual Display ◽  
Mass Spring

There are different kinds of geometrical models and physical models used to simulate weft knitted fabrics nowadays, such as loop models based on Pierce, piecewise function, spline curve, mass-spring model, and finite element analyses (FEA). Weft knitting simulation technology, including modeling and yarn reality, has been widely adopted in fabric structure designing for the manufacturer. The technology has great potentials in both industries and dynamic virtual display. The present article is aimed to review the current development of 3-D simulation technique for weft knitted fabrics.

scholarly journals Effect of time complexities and variation of mass spring model parameters on surgical simulation

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Salina Sulaiman ◽  
Tan Sing Yee ◽  
Abdullah Bade
Keyword(s):  
Soft Tissue ◽  
Human Liver ◽  
Soft Tissues ◽  
Surgical Simulation ◽  
Model Parameters ◽  
Spring Model ◽  
Surgical Simulator ◽  
Tissue Model ◽  
Mass Spring Model ◽  
Mass Spring

Physically based models assimilate organ-specific material properties, thus they are suitable in developing a surgical simulation. This study uses mass spring model (MSM) to represent the human liver because MSM is a discrete model that is potentially more realistic than the finite element model (FEM). For a high-end computer aided medical technology such as the surgical simulator, the most important issues are to fulfil the basic requirement of a surgical simulator. Novice and experienced surgeons use surgical simulator for surgery training and planning. Therefore, surgical simulation must provide a realistic and fast responding virtual environment. This study focuses on fulfilling the time complexity and realistic of the surgical simulator. In order to have a fast responding simulation, the choice of numerical integration method is crucial. This study shows that MATLAB ode45 is the fastest method compared to 2nd ordered Euler, MATLAB ode113, MATLAB ode23s and MATLAB ode23t. However, the major issue is human liver consists of soft tissues. In modelling a soft tissue model, we need to understand the mechanical response of soft tissues to surgical manipulation. Any interaction between haptic device and the liver model may causes large deformation and topology change in the soft tissue model. Thus, this study investigates and presents the effect of varying mass, damping, stiffness coefficient on the nonlinear liver mass spring model. MATLAB performs and shows simulation results for each of the experiment. Additionally, the observed optimal dataset of liver behaviour is applied in SOFA (Simulation Open Framework Architecture) to visualize the major effect.

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