A Proposed Model for Creep Relaxation of Soft Gaskets in Bolted Joints at Room Temperature

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Ali A. Alkelani ◽  
Basil A. Housari ◽  
Sayed A. Nassar
Keyword(s):  
Mathematical Model ◽  
Room Temperature ◽  
Closed Form Solution ◽  
Load Level ◽  
Form Solution ◽  
Bolted Joints ◽  
Experimental Procedure ◽  
Proposed Model ◽  
Gasket Material ◽  
Over Time

A mathematical model is proposed for predicting the residual clamp load during creep and∕or relaxation in gasketed joints. An experimental procedure is developed to verify the proposed model for predicting the gasket relaxation under a constant compression, gasket creep under a constant stress, and gasket creep relaxation. To study gasket creep relaxation, a single-bolt joint is used. The bolt is tightened to a target preload and the clamp load decay due to gasket creep relaxation is observed over time under various preload levels. Experimental and analytical results are presented and discussed. The proposed model provides an accurate prediction of the residual clamp load as a function of time, gasket material, and geometric properties of the gasket. A closed form solution is formulated to determine the initial clamp load level necessary to provide the desired level of a steady state residual clamp load in the joint, by taking the gasket creep relaxation into account.

A Proposed Model for Predicting Clamp Load Loss Due to Gasket Creep Relaxation in Bolted Joints

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Basil A. Housari ◽  
Ali A. Alkelani ◽  
Sayed A. Nassar
Keyword(s):  
Joint Stiffness ◽  
Closed Form Solution ◽  
Load Level ◽  
Form Solution ◽  
Bolted Joints ◽  
Experimental Procedure ◽  
Proposed Model ◽  
Gasket Material ◽  
Improved Model ◽  
Over Time

An improved mathematical model is proposed for predicting clamp load loss due gasket creep relaxation in bolted joints, taking into consideration gasket behavior, bolt stiffness, and joint stiffness. The gasket creep relaxation behavior is represented by a number of parameters which has been obtained experimentally in a previous work. An experimental procedure is developed to verify the proposed model using a single-bolt joint. The bolt is tightened to a target preload and the clamp load loss due to gasket creep relaxation is observed over time under various preload levels. The experimental and analytical results are presented and discussed. The proposed model provides a prediction of the residual clamp load as a function of time, gasket material and thickness, bolt stiffness, and joint stiffness. The improved model can be used to simulate the behavior of creep relaxation in soft joints as the joint stiffness effect is considered. Additionally, a closed form solution is formulated to determine the initial clamp load level necessary to provide the desired level of a steady state residual clamp load in the joint, by taking the gasket creep relaxation into account.

A Proposed Model for Predicting Residual Clamp Load in Gasketed Bolted Joints

2010 ◽  
Author(s):  
Basil A. Housari ◽  
Ali A. Alkelani ◽  
Sayed A. Nassar
Keyword(s):  
Joint Stiffness ◽  
Closed Form Solution ◽  
Load Level ◽  
Form Solution ◽  
Relaxation Behavior ◽  
Bolted Joints ◽  
Experimental Procedure ◽  
Proposed Model ◽  
Gasket Material ◽  
Improved Model

An improved mathematical model is proposed for predicting the residual clamp load in gasketed bolted joints, taking into consideration gasket creep relaxation behavior, bolt stiffness, and joint stiffness. The gasket creep relaxation behavior is represented by a number of parameters which has been obtained experimentally in a previous work. An experimental procedure is developed to verify the proposed model using a single-bolt joint. The bolt is tightened to a target preload and the clamp load loss due to gasket creep relaxation is observed over time under various preload levels. The experimental and analytical results are presented and discussed. The proposed model provides a prediction of the residual clamp load as a function of time, gasket material and thickness, bolt stiffness, and joint stiffness. The improved model can be used to simulate the behavior of creep relaxation in soft joints as the joint stiffness effect is considered. Additionally, a closed form solution is formulated to determine the initial clamp load level necessary to provide the desired level of a steady state residual clamp load in the joint, by taking the gasket creep relaxation into account.

Viscoelastic Strain Hardening Model for Gasket Creep Relaxation

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Antoine Abboud ◽  
Sayed A. Nassar
Keyword(s):  
Strain Hardening ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Duration ◽  
Experimental Procedure ◽  
Hardening Model ◽  
Pressure Step ◽  
Viscoelastic Strain ◽  
Step Loading ◽  
Gasket Material

This paper proposes a novel strain hardening model for investigating gasket creep relaxation under compressive step-loading at room temperature. A closed form solution is developed for predicting the steady-state gasket pressure. Step-loading of the gasket may be directly achieved and controlled, or indirectly estimated through the bolt tightening and retightening torque. The effect of gasket material, time duration at each stress level, as well as the geometric parameters of the gasket are investigated. An experimental procedure and test setup are used to validate the proposed gasket model.

Formulation of a Strain Hardening Model for Gasket Creep Relaxation

2011 ◽  
Author(s):  
Antoine Abboud ◽  
Sayed A. Nassar
Keyword(s):  
Strain Hardening ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Duration ◽  
Experimental Procedure ◽  
Hardening Model ◽  
Pressure Step ◽  
Step Loading ◽  
Gasket Material ◽  
Set Up

This paper proposes a novel strain hardening model for investigating gasket creep relaxation under compressive step-loading at room temperature. A closed form solution is developed for predicting the steady-state gasket pressure. Step-loading of the gasket may be directly achieved and controlled, or indirectly estimated through the bolt tightening and re-tightening torque. The effect of gasket material, time duration at each stress level, as well as the geometric parameters of the gasket is investigated. An experimental procedure and test set-up are used to validate the proposed gasket model.

Flow Analysis and Modeling of Field-Controllable, Electro- and Magneto-Rheological Fluid Dampers

2005 ◽  
Vol 74 (1) ◽  
pp. 13-22 ◽  
Author(s):  
Xiaojie Wang ◽  
Faramarz Gordaninejad
Keyword(s):  
Theoretical Model ◽  
Flow Analysis ◽  
Closed Form Solution ◽  
Nonlinear Behavior ◽  
Form Solution ◽  
Proposed Model ◽  
Fluid Dampers ◽  
Magneto Rheological ◽  
Er Fluid ◽  
Theoretical Results

This study combines a fluid mechanics-based approach and the Herschel-Bulkley constitutive equation to develop a theoretical model for predicting the behavior of field-controllable, magneto-rheological (MR), and electro-rheological (ER) fluid dampers. The goal is to provide an accurate theoretical model for analysis, design, and development of control algorithms of MR/ER dampers. Simplified explicit expressions for closed-form solution of the pressure drop across a MR fluid valve are developed. The Herschel-Bulkley quasi-steady flow analysis is extended to include the effect of fluid compressibility to account for the nonlinear dynamic behavior of MR/ER fluid dampers. The advantage of this model is that it only depends on geometric and material properties of the MR/ER material and the device. The theoretical results are validated by an experimental study. It is demonstrated that the proposed model can effectively predict the nonlinear behavior of field-controllable fluid dampers.

Bending Effect in Concentric Bolted Joints Under Transverse Load

2013 ◽  
Author(s):  
Yosef Amir ◽  
Saravanakumar Iyyanar ◽  
Aravind Devali ◽  
Muniratnam Kumar
Keyword(s):  
Closed Form ◽  
Potential Risk ◽  
Closed Form Solution ◽  
Form Solution ◽  
Bolted Joints ◽  
Transverse Load ◽  
Catastrophic Failure ◽  
Bending Stress ◽  
Bolted Joint ◽  
Bending Effect

Bending stress calculation in eccentric bolted joints is a well-known process in the design of bolted joints. However, in a concentric bolted joint with transverse load, the existence of bending stress is generally not considered as critical. But in reality, there is a possibility of catastrophic failure of the bolt occurring in a concentric bolted joint as a result of the bending stress even before the joint looseness or before the bolt fracture under tension. The aim of this paper is to propose a closed form solution to predict the potential risk of this failure that could be developed particularly at moderate preload of the bolt. Three concentric bolted joint cases with M12, M10 and M8 with transverse load and external tension load were investigated; FEA and experimental results validated the closed form calculation.

scholarly journals An Efficient Algorithm for Learning Dictionary under Coherence Constraint

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Huang Bai ◽  
Sheng Li ◽  
Qianru Jiang
Keyword(s):  
Synthetic Data ◽  
Closed Form Solution ◽  
Form Solution ◽  
Gram Matrix ◽  
Audio Signals ◽  
Novel Approach ◽  
Representation Error ◽  
Proposed Model ◽  
Minimization Procedure ◽  
Series Of Experiments

Dictionary learning problem has become an active topic for decades. Most existing learning methods train the dictionary to adapt to a particular class of signals. But as the number of the dictionary atoms is increased to represent the signals much more sparsely, the coherence between the atoms becomes higher. According to the greedy and compressed sensing theories, this goes against the implementation of sparse coding. In this paper, a novel approach is proposed to learn the dictionary that minimizes the sparse representation error according to the training signals with the coherence taken into consideration. The coherence is constrained by making the Gram matrix of the desired dictionary approximate to an identity matrix of proper dimension. The method for handling the proposed model is mainly based on the alternating minimization procedure and, in each step, the closed-form solution is derived. A series of experiments on synthetic data and audio signals is executed to demonstrate the promising performance of the learnt incoherent dictionary and the superiority of the learning method to the existing ones.

Effect of Separating Load Eccentricity on the Clamp Load Loss in a Bolted Joint Using a Strain Hardening Model

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Sayed A. Nassar ◽  
Mohan Ganganala
Keyword(s):  
Equilibrium Point ◽  
Strain Hardening ◽  
Elastic Limit ◽  
Closed Form Solution ◽  
Tensile Load ◽  
Load Level ◽  
Form Solution ◽  
Clamping Force ◽  
Bolted Joint ◽  
Load Rate

A nonlinear model is proposed for studying the effect of the eccentricity of applied tensile forces on the clamp load loss in bolted joints that were initially tightened beyond the bolt elastic limit while the joint remained in the elastic range. A closed form solution is obtained for the amount of clamp load loss due to a cyclic separating force. The proposed model takes into account two sources of nonlinearity, namely, the strain hardening behavior of the yielded bolt material as well as the nonlinear deformation behavior of the clamped plates under an external separating load. After the initial tightening of the fastener past its elastic limit, the subsequent application of a tensile separating force on the joint tends to increase the fastener tension in a nonlinear fashion, and, simultaneously, reduce the clamping force in the bolted joint from its initial value. Upon the removal of the cyclic tensile load, the bolted joint system reaches a new equilibrium point between the residual fastener tension and the joint clamping force. At the new equilibrium point, the fastener tension is reduced from its preload due to its plastic elongation; simultaneously, a partial yet permanent loss in the clamp load level takes place. Excessive clamp load loss may lead to joint leakage, fastener loosening, or fatigue failure. For a known amplitude of the external cyclic tensile load, the increase in bolt tension and corresponding reduction in the joint clamp load are highly sensitive to the eccentricity of the tensile load (from the bolt center). Variables studied include the eccentricity value of the separating load, rate of strain hardening of the bolt material, compressive and tensile stiffness of the clamped plates, bolt stiffness, bolt preload, and magnitude of the separating tensile load.

A Novel Formulation of Elastic Interaction in Gasketed Bolted Joints

2007 ◽  
Author(s):  
Ali A. Alkelani ◽  
Sayed A. Nassar ◽  
Basil A. Housari
Keyword(s):  
Mathematical Model ◽  
Load Distribution ◽  
Elastic Interaction ◽  
Bolted Joints ◽  
Good Prediction ◽  
Proposed Model ◽  
Joint Tightening ◽  
The Mathematical Model ◽  
Bolt Spacing ◽  
Initial Assembly

A novel mathematical model is proposed for studying elastic interaction in gasketed bolted joints. The model predicts the tension changes in tightened bolts due to the subsequent tightening of other bolts in the joint. It also predicts the final clamp load distribution after the completion of joint tightening. The model is used to investigate the effect of various factors on the elastic interaction phenomenon; factors include the gasket thickness, bolt spacing, fastener preload level, and the tightening sequence of various bolts. Experimental verification is provided for the validation of the mathematical model. Experimental and analytical results are presented and discussed. The proposed model provides good prediction of the final clamp load in the joint. Moreover, the proposed model may be used to determine the level of initial bolt tension in each bolt that would be necessary to achieve the desired level of uniform clamp load in the joint at initial assembly.

Mathematical Model for Closed-Form Solution of Parameters of Cylinder Exhaust Port in Variable-Stroke Engine

2010 ◽  
Vol 97-101 ◽  
pp. 2724-2727
Author(s):  
Li Ming Di ◽  
Chun Jing Yang ◽  
Yong Sheng Zhao
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Alignment Method ◽  
Specific Time ◽  
Exhaust Port ◽  
Initial Stage ◽  
Relative Errors ◽  
Stroke Engine

A mathematical model for getting the closed-form solution of main parameters of cylinder exhaust port is present, based on a few known parameters of variable-stroke engine (VSE). Considering lack of parameters in the initial stage of design, empirical formula is applied to solve the initial specific time-area value of exhaust port, and the initial port timing angle is solved by using logarithmic alignment method, thereby height and width of the exhaust port can be solved, then the precise specific time-area value and port timing angle are solved by using the coefficient calculation method and logarithmic alignment method respectively, so that the relative errors between initial and precise values of specific time-area value and port timing angle are defined as the relative errors of the mathematical model. Application examples show that the relative errors of the model is less than 3%.

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