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.

scholarly journals Study on Gear Contact Stiffness and Backlash of Harmonic Drive Based on Fractal Theory

2021 ◽  
Author(s):  
Tao Zhang ◽  
Zhifeng Liu ◽  
Congbin Yang ◽  
Yang Wang ◽  
Qianqian Liu
Keyword(s):  
Contact Force ◽  
Contact Stiffness ◽  
Fractal Theory ◽  
Roughness Parameter ◽  
Tooth Surface ◽  
Gear Backlash ◽  
Fractal Parameters ◽  
Fractal Roughness ◽  
Gear Contact ◽  
Tooth Pair

Abstract Contact stiffness and backlash model of harmonic reducer is related to robot’s positioning accuracy and vibration characteristics. Harmonic reducer tooth pair height is typically less than 1 mm. Thus, backlash and contact stiffness measurement and modeling are relatively complex. In this paper, contact stiffness and backlash model is proposed by establishing a relationship between fractal parameters and tooth contact load. Non-contact optical profiler and RMS method are combined to obtain fractal roughness parameters of real machined tooth surface. Finally, the effect of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash is studied. The results indicate that surface topography parameters and contact force have significant effects on contact stiffness and backlash. By increasing the fractal dimension, a decrease of gear backlash and contact stiffness is observed. However, the opposite is true for the fractal roughness parameter. Lastly, an increase in contact force improves the contact stiffness.

Experimental Observation of Fractal-Regular Surfaces and a Transformation Scheme for Extracting Fractal Parameters

2005 ◽  
Author(s):  
Shao Wang ◽  
Wai Kin Chan
Keyword(s):  
Silicon Wafer ◽  
Roughness Parameter ◽  
Hard Disk ◽  
Spectral Density Function ◽  
Power Spectral ◽  
Fractal Parameters ◽  
Asperity Contacts ◽  
Fractal Roughness ◽  
Magnetic Hard Disk ◽  
Wafer Surfaces

To account for the effects of asperity contacts at various length scales, it is appropriate to characterize an engineering surface as a fractal-regular surface. In spite of significant theoretical advancement, there is a desperate need for experimental verification of the theory of fractal-regular surfaces and a consistent scheme of obtaining the fractal parameters. In the present study, the existence of a fractal region and a regular-shape region in the power spectral density function for fractal-regular surfaces was confirmed experimentally, for the first time, with data obtained from magnetic hard disk and silicon wafer surfaces. A novel scheme involving a variable transformation was developed to extract fractal parameters. This scheme was validated by accurate recovery of fractal parameters from simulated surfaces. The fractal dimension, the fractal roughness parameter and the fractal domain length were found for magnetic hard disk and silicon wafer surfaces.

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.

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.

A Method to Determine the Fractal Roughness Parameter from Surface Profiles Generated by the WM Function

2013 ◽  
Vol 341-342 ◽  
pp. 329-332 ◽  
Author(s):  
Li Wang ◽  
Yang Xiang
Keyword(s):  
Fractal Dimension ◽  
Numerical Scheme ◽  
Function Method ◽  
Roughness Parameter ◽  
Surface Profile ◽  
Reasonable Accuracy ◽  
Characteristic Parameters ◽  
Fractal Surface ◽  
Fractal Roughness ◽  
Surface Profiles

The fractal surface profile can usually be represented by WM function, A fractal dimension and a fractal roughness parameter are very important characteristic parameters in WM function. Usually, fractal scaling parameter γ was set to equal to 1.5, fractal dimension can be determined by the structure function method, but the accurately identification of the fractal roughness parameter is still a problem. In the present study, a simply numerical scheme with clear routine was developed to determine the fractal roughness parameter, and the fractal roughness parameter were recovered with reasonable accuracy from the numerically generated rough surface profile based WM function.

scholarly journals Fractal dimension confidence interval estimation of epicentral distributions

1999 ◽  
Vol 42 (5) ◽  
Author(s):  
L. De Luca ◽  
S. Lasocki ◽  
D. Luzio ◽  
M. Vitale
Keyword(s):  
Fractal Dimension ◽  
Confidence Intervals ◽  
Seismic Data ◽  
Interval Estimation ◽  
Fractal Dimensions ◽  
Data Sets ◽  
Independent Variables ◽  
Fractal Parameters ◽  
Confidence Interval Estimation ◽  
Selection Of

Estimates of the fractal dimension of hypocentral distributions require evaluating the range of independent variables in which fractal parameters exhibit a power law. Systematic and accidental errors are produced mainly by the subjective selection of this range, the insufficiency of data sets as well as by hypocenter mislocations. Therefore it is very important to determine the confidence intervals which are associated with fractal dimension estimates. The effects of various sources of errors are studied using different geometric clusters of epicenters, which have been synthetically generated using a multicluster algorithm with different hierarchical levels, so as to reproduce some characteristics of the patterns typical of real epicenter distributions. Subsequently, groups of differently sized subsets of synthetic epicenters were obtained by randomly sampling each distribution. Confidence intervals of fractal dimensions were thus calculated using all the estimates obtained for the various subsets. This procedure was also tested on real seismic data, consisting of epicentral distributions in three Sicilian areas and five clusters of mining-induced seismic events (Wujek coal mine, Poland). In that analysis both correlation dimensions and their confidence intervals were taken into account.

Stiffness and damping model of bolted joint based on the modified three-dimensional fractal topography

2016 ◽  
Vol 231 (2) ◽  
pp. 279-293 ◽  
Author(s):  
Yongsheng Zhao ◽  
Jingjing Xu ◽  
Ligang Cai ◽  
Weimin Shi ◽  
Zhifeng Liu
Keyword(s):  
Contact Surface ◽  
Machine Tools ◽  
Contact Stiffness ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Roughness Parameter ◽  
Mode Shapes ◽  
Real Contact Area ◽  
Bolted Joint ◽  
Stiffness And Damping

The machine tools are consisted of many parts and most of them are connected by the bolts. Accurate modeling of contact stiffness and damping for bolted joint is crucial in predicting the dynamic performance of machine tools. This paper presents a modified three-dimensional fractal contact model to obtain the stiffness and damping of bolted joint. Topography of the contact surface of bolted joint is fractal featured and determined by fractal parameters. Asperities in microscale are considered as elastic, elastic–plastic, and full plastic deformation. The expand coefficient ψ is introduced to the size-distribution function of asperities. The real contact area, contact stiffness, and damping of the contact surface can be calculated by integrating the microasperities. The relationship of contact stiffness, damping, fractal dimension D, and fractal roughness parameter G can be obtained. Experiments are conducted to verify the efficiency of the proposed model. The results show that the theoretical mode shapes are in good agreement with the experimental mode shapes. The relative errors between the theoretical and experimental natural frequencies are less than 3.33%, which is less than those of the W-K model and L-L model. The presented model can be used to accurately predict the dynamic characteristic of bolted assembly in the machine tools.

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.

Viscous Friction Effect During the Process of Tightening and Loosening of Bolted Joints

2021 ◽  
Author(s):  
Qingyuan Lin ◽  
Yong Zhao ◽  
Qingchao Sun ◽  
Kunyong Chen
Keyword(s):  
Friction Coefficient ◽  
Viscous Friction ◽  
Normal Pressure ◽  
Friction Model ◽  
Bolted Joints ◽  
Critical Parameters ◽  
Bolted Joint ◽  
Sliding Velocity ◽  
Friction Effect ◽  
Bearing Friction

Abstract Bolted connection is one of the most widely used mechanical connections because of its easiness of installation and disassembly. Research of bolted joints mainly focuses on two aspects: high precision tightening and improvement of anti-loosening performance. The under-head bearing friction coefficient and the thread friction coefficient are the two most important parameters that affect the tightening result of the bolted joint. They are also the most critical parameters that affect the anti-loosening performance of the bolted joint. Coulomb friction model is a commonly used model to describe under-head bearing friction and thread friction, which considers the friction coefficient as a constant independent of normal pressure and relative sliding velocity. In this paper, the viscous effect of the under-head bearing friction and thread friction is observed by measuring the friction coefficient of bolted joints. The value of the friction coefficient increases with the increase of the relative sliding velocity and the decrease of the normal pressure. It is found that the Coulomb viscous friction model can better describe the friction coefficient of bolted joints. Taking into account the dense friction effect, the loosening prediction model of bolted joints is modified. The experimental results show that the Coulomb viscous friction model can better describe the under-head bearing friction coefficient and thread friction coefficient. The model considering the dense effect can more accurately predict the loosening characteristics of bolted joints.

scholarly journals Development of Novel Fractal Method for Characterizing the Distribution of Blood Flow in Multi-Scale Vascular Tree

2021 ◽  
Vol 12 ◽  
Author(s):  
Peilun Li ◽  
Qing Pan ◽  
Sheng Jiang ◽  
Molei Yan ◽  
Jing Yan ◽  
...  
Keyword(s):  
Blood Flow ◽  
Fractal Dimension ◽  
Flow Distribution ◽  
Multifractal Spectrum ◽  
Vascular Structure ◽  
Blood Flow Distribution ◽  
Vascular Tree ◽  
Multi Scale ◽  
Fractal Parameters ◽  
Vascular Trees

Blood perfusion is an important index for the function of the cardiovascular system and it can be indicated by the blood flow distribution in the vascular tree. As the blood flow in a vascular tree varies in a large range of scales and fractal analysis owns the ability to describe multi-scale properties, it is reasonable to apply fractal analysis to depict the blood flow distribution. The objective of this study is to establish fractal methods for analyzing the blood flow distribution which can be applied to real vascular trees. For this purpose, the modified methods in fractal geometry were applied and a special strategy was raised to make sure that these methods are applicable to an arbitrary vascular tree. The validation of the proposed methods on real arterial trees verified the ability of the produced parameters (fractal dimension and multifractal spectrum) in distinguishing the blood flow distribution under different physiological states. Furthermore, the physiological significance of the fractal parameters was investigated in two situations. For the first situation, the vascular tree was set as a perfect binary tree and the blood flow distribution was adjusted by the split ratio. As the split ratio of the vascular tree decreases, the fractal dimension decreases and the multifractal spectrum expands. The results indicate that both fractal parameters can quantify the degree of blood flow heterogeneity. While for the second situation, artificial vascular trees with different structures were constructed and the hemodynamics in these vascular trees was simulated. The results suggest that both the vascular structure and the blood flow distribution affect the fractal parameters for blood flow. The fractal dimension declares the integrated information about the heterogeneity of vascular structure and blood flow distribution. In contrast, the multifractal spectrum identifies the heterogeneity features in blood flow distribution or vascular structure by its width and height. The results verified that the proposed methods are capable of depicting the multi-scale features of the blood flow distribution in the vascular tree and further are potential for investigating vascular physiology.

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