A stiffness model for bolted joints considering asperity interactions of rough surface contact

2021 ◽  
pp. 1-20
Author(s):  
Hua Zhou ◽  
Xinhua Long ◽  
Guang Meng ◽  
Xianbo Liu
Keyword(s):  
Contact Stiffness ◽  
Classical Model ◽  
Surface Profile ◽  
Bolted Joints ◽  
Normal Stiffness ◽  
Proposed Model ◽  
Stiffness Model ◽  
Fractal Roughness ◽  
Rough Surface Contact ◽  
Stiffness Loss

Abstract A revised fractal contact model considering asperity interactions is proposed. The displacement of mean of asperity heights is used to represent the effects of the asperity interactions. Then the critical contact area will be dependent on the contact load and the contact stiffness will be an integral whose integrand is an implicit expression. The fractal dimension and the fractal roughness are obtained by the measurement of surface profile to calculate the theoretical contact stiffness. The measurement of deformation is conducted to obtain the actual contact stiffness for verification, the results show that the proposed model is closer to the experimental results than other models without considering asperity interactions. Once the contact stiffness is determined, a new total normal stiffness model for bolted joints considering the contact of two rough surfaces is also proposed. Since the contact stiffness is dependent on the clamped force, the total normal stiffness for bolted joints is calculated iteratively at given initial preload and external separating force. Different from the classical model, the total normal stiffness for bolted joint decreases with the external separating force increases, and this stiffness loss will become larger with initial preload decreases. In this sense, the proposed total normal stiffness model is a way to determine the suitable initial preload for different sizes of bolts when the stiffness loss is restricted to a certain range.

Stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities

2019 ◽  
Vol 72 (1) ◽  
pp. 128-135 ◽  
Author(s):  
Hongxu Chen ◽  
Qin Yin ◽  
Guanhua Dong ◽  
Luofeng Xie ◽  
Guofu Yin
Keyword(s):  
Elastic Deformation ◽  
Contact Stiffness ◽  
Roughness Parameter ◽  
Experimental Results ◽  
Content Type ◽  
Elastoplastic Contact ◽  
Proposed Model ◽  
Stiffness Model ◽  
Fractal Roughness ◽  
Deformation Ratio

Purpose The purpose of this paper is to establish a stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities. Design/methodology/approach The proposed model considers that asperities of different scales are interrelated rather than independent. For elastoplastic contact, a spring-damper model and an elastic deformation ratio function were proposed to calculate the contact stiffness of asperities. Findings A revised fractal asperity model was proposed to calculate the contact stiffness of fixed joint, the impacts of the fractal dimension, the fractal roughness parameter and the Meyer index on the contact stiffness were discussed, and the present experimental results and the Jiang’s experimental results showed that the stiffness can be well predicted by proposed model. Originality/value The contradiction between the Majumdar and Bhushan model and the Morag and Etsion model can be well explained by considering the interaction among asperities of different scales. For elastoplastic contact, elastic deformation ratio should be considered, and the stiffness of asperities increases first and then decreases with the increasing of interference.

Physics-Based Modeling for Lap-Type Joints Based on the Iwan Model

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Wanglong Zhan ◽  
Ping Huang
Keyword(s):  
Distribution Function ◽  
Constitutive Relations ◽  
Hysteresis Loops ◽  
Experimental Results ◽  
Bolted Joints ◽  
Height Distribution ◽  
Proposed Model ◽  
Contact Situation ◽  
Rough Surface Contact ◽  
Nonlinear Constitutive Relation

This study proposed a physics-based heuristic modeling for the nonlinear constitutive relation of bolted joints based on the Iwan model accompanying with the rough surface contact theory. The approach led to an Iwan distribution function which possesses the tribology-related features of the contact interface. In particular, the break-free force distribution function of the Jenkins elements could be expressed in terms of height distribution of surface asperities. The model considered the contribution of elastically, elasto-plastically as well as plastically deformed asperities to the total tangential loads. Following this, constitutive relations for lap-type bolted joints and the corresponding backbone curves, hysteresis loops, and energy dissipation per cycle were obtained. A model application was implemented and the results were compared with the published experimental results. The proposed model agrees very well with the experimental results when the contact parameters met the actual contact situation. The obtained results indicated that the model can be used to study the tangential behaviors of rough surfaces.

Elastic Contact Model Accounting for Both Asperity and Substrate Compliance With Application to Patterned Media

2007 ◽  
Author(s):  
Chang-Dong Yeo ◽  
Andreas A. Polycarpou
Keyword(s):  
Bulk Material ◽  
Contact Stiffness ◽  
Contact Model ◽  
Elastic Contact ◽  
Element Analysis ◽  
Patterned Media ◽  
Single Asperity ◽  
Proposed Model ◽  
Stiffness Model ◽  
Bulk Substrate

An improved elastic contact stiffness model for a single asperity system is proposed to account for the effects of both bulk substrate and asperity deformations between two contacting surfaces. Depending upon the applied load, as well as the geometrical and physical properties of the asperity and bulk material, the bulk substrate can have a considerable contribution to the overall contact stiffness. Finite element analysis is performed to verify the proposed analytical model. The single asperity model is extended to rough surfaces in contact. The contact stiffness values from the proposed model are compared to those from the GW model. The proposed contact model can be directly relevant to analyze the contact behavior of modern patterned media.

An improved stiffness model for line contact elastohydrodynamic lubrication and its application in gear pairs

2020 ◽  
Vol 72 (5) ◽  
pp. 703-708 ◽  
Author(s):  
Jiaxing Pei ◽  
Xu Han ◽  
Yourui Tao
Keyword(s):  
External Load ◽  
Contact Stiffness ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Content Type ◽  
Meshing Stiffness ◽  
Proposed Model ◽  
Stiffness Model ◽  
Film Stiffness ◽  
Ehl Contact

Purpose The purpose of this paper is to propose an simple and efficient stiffness model for line contact under elastohydrodynamic lubrication (EHL) and to investigate the gear meshing stiffness by the proposed model. Design/methodology/approach The method combines the surface contact stiffness and film stiffness as EHL contact stiffness. The EHL contact stiffness can be calculated by the external load and displacement of the load action point. The displacement is the sum of deformation of the film and contact surface and is equal to the distance of the mutual approach of two contact bodies. Findings The conclusion is drawn that the contact stiffness calculated by the proposed model is smaller than that by the minimum film model and larger than that by the mean film model. It is also concluded that the gear meshing stiffness under EHL is slightly smaller than that under dry contact. Originality/value The EHL contact stiffness can be obtained by the increment of external load and mutual approach directly. The calculation of oil film stiffness and surface contact stiffness separately is avoided. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0465

A MODIFIED COMPLETE NORMAL CONTACT STIFFNESS MODEL OF A FRACTAL SURFACE CONSIDERING CONTACT FRICTION

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050081
Author(s):  
CHUNLING WEI ◽  
HUA ZHU ◽  
SHIHUI LANG
Keyword(s):  
Contact Stiffness ◽  
Fractal Dimensions ◽  
Frictional Resistance ◽  
Contact Model ◽  
Contact Friction ◽  
Fractal Surface ◽  
Normal Contact ◽  
Stiffness Model ◽  
Fractal Roughness ◽  
Normal Contact Stiffness

This paper presents a modified complete normal contact stiffness model of a fractal surface considering contact friction. We use this model to study the influence of fractal dimensions and fractal roughness on normal contact stiffness. The fractal micro-contact model of an asperity and the complete length scale contact model of fractal surface (both contrasting classical mechanics) are revised. The influence of frictional resistance at micro-contact interfaces on normal contact stiffness is also considered. Predictions of the new model are found to be in greater agreement with the results of the experiments than the predictions of the original model. The study analyzes the influence of fractal dimensions and fractal roughness on the normal contact stiffness. With the increase of these two fractal parameters, their influences on the normal contact stiffness are opposite and are different under high pressure and low pressure.

A Contact Stiffness Model of Machined Plane Joint Based on Fractal Theory

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Shuyun Jiang ◽  
Yunjian Zheng ◽  
Hua Zhu
Keyword(s):  
Contact Stiffness ◽  
Fractal Theory ◽  
Fractal Model ◽  
Experimental Results ◽  
Size Dependent ◽  
Contact Loads ◽  
Proposed Model ◽  
Stiffness Model ◽  
Surface Profiles ◽  
Plane Joint

A general contact stiffness model is proposed in this paper to study the contacts between rough surfaces of machined plane joints. The proposed model uses fractal geometry for surface topography description, elastic-plastic deformation of contacting asperities, and size-dependent contact stiffness of microcontacts, where the contact stiffness is derived from Hertz contact theory. Three cast iron specimens are produced from different machining methods (milling, grinding, and scraping), and their rough surface profiles are extracted. The structure function method was used to calculate each profile’s fractal dimension and scale coefficient. Both theoretical analysis and experimental results of contact stiffness are obtained for these specimens under different contact loads. The comparison between the theoretical contact stiffness and the experimental results at the interface indicates that the present fractal model for the contact stiffness is appropriate and the theoretical contact stiffness is consistent with the experimental data.

scholarly journals Interval estimation for contact stiffness of bolted joint with uncertain parameters

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401988370 ◽  
Author(s):  
Yongsheng Zhao ◽  
Hongchao Wu ◽  
Congbin Yang ◽  
Zhifeng Liu ◽  
Qiang Cheng
Keyword(s):  
Fractal Dimension ◽  
Contact Surface ◽  
Contact Stiffness ◽  
Interval Estimation ◽  
Roughness Parameter ◽  
Normal Pressure ◽  
Bolted Joints ◽  
Uncertain Parameters ◽  
Fractal Parameters ◽  
Fractal Roughness

Bolted joints are elements used to create resistant assemblies in the mechanical system, whose overall performance is greatly affected by joints’ contact stiffness. Most of the researches on contact stiffness are based on certainty theory whereas in real applications the uncertainty characterizes the parameters such as fractal dimension D and fractal roughness parameter G. This article presents an interval estimation theory to obtain the stiffness of bolted joints affected by uncertain parameters. Topography of the contact surface is fractal featured and determined by fractal parameters. Joint stiffness model is built based on the fractal geometry theory and contact mechanics. Topography of the contact surface of bolted joints is measured to obtain the interval of uncertain fractal parameters. Equations with interval parameters are solved to acquire the interval of contact stiffness using the Chebyshev interval method. The relationship between the interval of contact stiffness and the uncertain parameters, that is, fractal dimension D, fractal roughness parameter G, and normal pressure, can be obtained. The presented model can be used to estimate the interval of stiffness for bolted joints in the mechanical systems. The results can provide theoretical reference for the reliability design of bolted joints.

A multi-scale stiffness fractal model of joint interfaces

2021 ◽  
pp. 81-95
Author(s):  
Jingfang Shen ◽  
◽  
Sijie Cheng ◽  
Siyan Wang ◽  
Wenwei Liu ◽  
...  
Keyword(s):  
Contact Mechanics ◽  
Normal Load ◽  
Contact Stiffness ◽  
Roughness Parameter ◽  
Numerical Control ◽  
Joint Interface ◽  
Normal Contact ◽  
Multi Scale ◽  
Stiffness Model ◽  
Fractal Roughness

Stiffness characterization of mechanical interfaces is quite crucial for the analysis of several tribological behaviors. The stiffness of different machine tools varies greatly, particularly for computer numerical control machine. Therefore, this research aims at providing an assessment of influence factors for stiffness of joint interfaces theoretically. Based on fractal roughness parameters independent of scale and contact mechanics theory, the contact area of joint interface is studied, and the multi-scale normal contact stiffness model and multi-scale tangential contact stiffness model are proposed. Meanwhile, the problem of the deformation of any contact asperity is considered as three separate regimes. The laws of area-displacement and force-displacement under elastic-plastic regime are established. The transition which is in the deformation mechanism of asperity from elastic to plastic is consistent with classical contact mechanics. The analysis of numerical calculation results indicates the approximate linear relation among dimensionless normal load and key parameters. Moreover, these key parameters have been divided into two main categories for the multiscale model of joint interfaces, one is fractal parameters such as fractal dimension D and fractal roughness parameter G, and the other is interfacial parameters. In addition, tangential load and friction factor are two important factors to the tangential stiffness.

An Expanded Model for the Application of Parametric Statistics

1976 ◽  
Vol 39 (1) ◽  
pp. 311-318
Author(s):  
Jack Hand ◽  
Robert E. McCarter
Keyword(s):  
Current Model ◽  
Classical Model ◽  
Proposed Model ◽  
Parametric Statistics

The current model for the application of parametric statistics involves only the population sampled, and probability statements refer to proportions of samples or proportions of decisions based upon samples. Most statistical textbooks, however, contain concepts that go beyond the explicitly proposed model. The rudiments of an appropriate, expanded model are presented. It is suggested that the expanded model is more adequate, general, and realistic than the classical model.

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